divide

-3x<= -9 or 5+x<6 Take each piece: -3x<= -9 Divide each side by -3: x>=3 Now take 5 + x < 6 5 + x < 6 Subtract 5 from each side: x < 1 Joining together the two inequalities, we have: x<1 or x>=3 Use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3C1orx%3E%3D3&pl=Show+Interval+Notation']interval notion calculator[/URL] to find the interval notation of this compound inequality

-5n - 5n - 5 = 5 Solve for [I]n[/I] in the equation -5n - 5n - 5 = 5 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (-5 - 5)n = -10n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -10n - 5 = + 5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -5 and 5. To do that, we add 5 to both sides -10n - 5 + 5 = 5 + 5 [SIZE=5][B]Step 4: Cancel 5 on the left side:[/B][/SIZE] -10n = 10 [SIZE=5][B]Step 5: Divide each side of the equation by -10[/B][/SIZE] -10n/-10 = 10/-10 n = [B]- 1 [URL='https://www.mathcelebrity.com/1unk.php?num=-5n-5n-5%3D5&pl=Solve']Source[/URL][/B]

-g + 3/4a = y for a Add g to each side: -g + g + 3/4a = y + g Cancel the g terms on the left side: 3/4a = y + g Cross multiply: 3a = 4(y + g) Divide each side by 3 to isolate a: 3a/3 = 4(y + g)/3 a = [B]4(y + g)/3[/B]

-g+F/A=h^3 for A Add g to each side: -g + g+F/A=h^3 + g Cancel the g's on the left side: F/A = h^3 + g Cross multiply: F = A(h^3 + g) Divide each side by (h^3 + g) F/(h^3 + g) = A(h^3 + g)/(h^3 + g) Cancel (h^3 + g) on the right side: A = [B]F/(h^3 + g)[/B]

1 - n = n - 1 Solve for [I]n[/I] in the equation 1 - n = n - 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -n and n. To do that, we subtract n from both sides -n + 1 - n = n - 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] -2n + 1 = -1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 1 and -1. To do that, we subtract 1 from both sides -2n + 1 - 1 = -1 - 1 [SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE] -2n = -2 [SIZE=5][B]Step 5: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = -2/-2 n = [B]1 [URL='https://www.mathcelebrity.com/1unk.php?num=1-n%3Dn-1&pl=Solve']Source[/URL][/B]

1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers. Let the first integer be x and the second integer be y. We have the following two equations: [LIST=1] [*]x = 7y [*]xy = 448 [/LIST] Substitute (1) into (2), we have: (7y)y = 448 7y^2 = 448 Divide each side by 7 y^2 = 64 y = -8, 8 We use 8, since 8*7 = 56, and 56*8 =448. So the answer is [B](x, y) = (8, 56)[/B]

1/2 the difference of x and 4 The difference of x and 4: x - 4 1/2 of the difference means we divide x -4 by 2: [B](x - 4)/2[/B]

1/2n + 1&1/2n = -10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%261%2F2&frac2=3%2F8&pl=Simplify']1&1/2 = 3/2[/URL] so we have: n/2 + 3n/2 = -10 4n/2 = -10 2n = -10 Divide each side by 2: 2n/2 = -10/2 n = [B]-5[/B]

1/3ab^2=6 for a Multiply each side by 3: ab^2 = 18 Divide each side by b^2 a = 18/b^2

1/4 of the difference of 6 and a number is 200 Take this [B]algebraic expression[/B] in 4 parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The difference of 6 and a number means we subtract x from 6: 6 - x [*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4 [*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200 [/LIST] [B](6 - x)/4 = 200[/B]

1/a + 1/b = 1/2 for a Subtract 1/b from each side to solve this literal equation: 1/a + 1/b - 1/b = 1/2 - 1/b Cancel the 1/b on the left side, we get: 1/a = 1/2 - 1/b Rewrite the right side, using 2b as a common denominator: 1/a = (b - 2)/2b Cross multiply: a(b - 2) = 2b Divide each side by (b - 2) a = [B]2b/(b - 2)[/B]

1/n + 3/5 = 1 Subtract 3/5 from each side where 1 = 5/5 1/n + 3/5 - 3/5 = 5/5 - 3/5 1/n = 2/5 Cross multiply: 5 * 1 = 2 * n 2n = 5 Divide each side by 2: n = [B]5/2 or 2.5[/B]

1/n^2 = 3/192 Cross multiply: 192 * 1 = 3 * n^2 3n^2 = 192 Divide each side by 3: 3n^2/3 = 192/3 Cancel the 3's on the left side: n^2 = 64 Take the square root of both sides: n = [B]8 or -8[/B]

10 divided by the sum of 4 and u Take this algebraic expression in parts: The sum of 4 and u means we add 4 to u: 4 + u Next, we divide 10 by this sum: [B]10/(4 + u)[/B]

10 more than a number z, divided by k The phrase [I]a number[/I] means an arbitrary variable, lets call it x. 10 more than a number means we add 10 to x: x + 10 We divide this quantity by k: [B](x + 10)/k[/B]

10 times the square of a number w divided by 12 The square of a number w w^2 10 times this 10w^2 Divided by 12 [B]10w^2/12[/B]

10 x 12 divided by 9 12/9 1.3333333 Then multiply by 10: [B]13.33333333[/B]

100n = 100 Solve for [I]n[/I] in the equation 100n = 100 [SIZE=5][B]Step 1: Divide each side of the equation by 100[/B][/SIZE] 100n/100 = 100/100 n = [B]1[/B]

10ac-x/11=3 for a Add x/11 to each side of the equation to isolate a: 10ac - x/11 + x/11 = 3 + x/11 Cancelling the x/11 on the left side, we get: 10ac = 3 + x/11 Divide each side by 10c to isolate a: 10ac/10c = 3 + x/11 Cancelling the 10c on the left side, we get: a = [B]3/10c + x/110c[/B]

10n - 9n + 8n - 7n + 6n = 10 - 9 + 8 - 7 + 6 Solve for [I]n[/I] in the equation 10n - 9n + 8n - 7n + 6n = 10 - 9 + 8 - 7 + 6 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (10 - 9 + 8 - 7 + 6)n = 8n [SIZE=5][B]Step 2: Group the constant terms on the right hand side:[/B][/SIZE] 10 - 9 + 8 - 7 + 6 = 8 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 8n = + 8 [SIZE=5][B]Step 4: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 8/8 n = [B]1[/B]

10n = 0.5 Solve for [I]n[/I] in the equation 10n = .5 [SIZE=5][B]Step 1: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = .5/10 n = [B]0.05 [URL='https://www.mathcelebrity.com/1unk.php?num=10n%3D.5&pl=Solve']Source[/URL][/B]

12 divided into groups of s We build our algebraic expression as follows: [B]12/s[/B]

15y + 13/c = m for y Subtract 13/c from each side to isolate the y term: 15y + 13/c - 13/c = m - 13/c Cancel the 13/c on the left side and we get 15y = m - 13/c Now, divide each side by 15 to isolate y: 15y/15 = (m - 13/c)/15 Cancel the 15 on the left side, and we get: y = [B](m - 13/c)/15[/B]

175/n = 25 25n = 175 Divide each side by 25 [B]n = 7 classes[/B]

175 students separated into n classes is 25 [U]Divide 175 by n[/U] 175/n [U]The word [I]is[/I] means equal to, so set this expression equal to 25[/U] 175/n = 25 [U]Cross multiply[/U] 25n = 175 [U]Divide each side by 25[/U] [B]n = 7[/B]

Let x be the first even integer. That means the next consecutive even integer must be x + 2. Set up our equation: x + (x + 2) = 118 Group x terms 2x + 2 = 118 Subtract 2 from each side 2x = 116 Divide each side by 2 x = 58 Which means the next consecutive even integer is 58 + 2 = 60 So our two consecutive even integers are [B]58, 60[/B] Check our work: 58 + 60 = 118

2 numbers that are equal have a sum of 60 Let's choose 2 arbitrary variables for the 2 numbers x, y Were given 2 equations: [LIST=1] [*]x = y <-- Because we have the phrase [I]that are equal[/I] [*]x + y = 60 [/LIST] Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add like terms to get: 2y = 60 Divide each side by 2: 2y/2 = 60/2 Cancel the 2's and we get: y = [B]30 [/B] Since x = y, x = y = 30 x = [B]30[/B]

A number means an arbitrary variable, let's call it x. Half of x means we divide x by 2, or multiply by 0.5 x/2 2 times half x is written: [B]2(x/2)[/B] If we simplify by cancelling the 2's, we just get x.

2 times the sum of 3 and 5 divided by 10 The sum of 3 and 5 is written as: 3 + 5 2 times this sum: 2(3 + 5) Then, we divide this by 10: [B]2(3 + 5)/10[/B] [B][/B] If the problem asks you to simplify this, you [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=2%283%2B5%29%2F10&pl=Perform+Order+of+Operations']type this expression into our search engine[/URL] and get: [B]1.6[/B]

2 times x divided by 4 times y 2 times x: 2x 4 times y: 4y 2 times x divided by 4 times y [B]2x/4y[/B]

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay? [U]Calculate Discount Percent:[/U] If the teachers got a 24% discount, that means they paid: 100% - 24% = 76% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent) [U]Calculate discount price:[/U] Discount Price = Full Price * (Discount Percent) Discount Price = 5230 * 0.76 Discount Price = 3974.80 Price per teacher = Discount Price / Number of Teachers Price per teacher = 3974.80 / 20 Price per teacher = [B]$198.74[/B]

$69.99 per apple / 200 apples We want the price per apple. Divide top and bottom by 200 $0.35 per apple.

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit We use our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=21&num2=49&num3=&pl=GCF+and+LCM']greatest common factor calculator for GCF(21, 49)[/URL] to get: GCF(21, 49) = 7 This means with [B]7 baskets[/B]: [LIST] [*]We divide 21 apples by 7 to get 3 apples per basket [*]We divide 49 pears by 7 to get 7 pears per basket [/LIST]

22 & 1/2 / 1/8 = 22 & 1/2 = 45/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F2&frac2=1%2F8&pl=Divide']45/2 / 1/8[/URL] = [B]180[/B]

2d = (a - b)/(b - c) for d Divide each side by 2 to isolate d: 2d/2 = (a - b)/2(b - c) Cancel the 2's on the left side, we get: d = [B](a - b)/2(b - c)[/B]

2n + 10 = 3n + 5 Solve for [I]n[/I] in the equation 2n + 10 = 3n + 5 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 3n. To do that, we subtract 3n from both sides 2n + 10 - 3n = 3n + 5 - 3n [SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE] -n + 10 = 5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 10 and 5. To do that, we subtract 10 from both sides -n + 10 - 10 = 5 - 10 [SIZE=5][B]Step 4: Cancel 10 on the left side:[/B][/SIZE] -n = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -5/-1 n = [B]5[/B]

2n + 8 = 24 Solve for [I]n[/I] in the equation 2n + 8 = 24 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 8 and 24. To do that, we subtract 8 from both sides 2n + 8 - 8 = 24 - 8 [SIZE=5][B]Step 2: Cancel 8 on the left side:[/B][/SIZE] 2n = 16 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 16/2 n = [B]8[/B]

2n - 1&1/2n = 59 1&1/2n = 3/2n or 1.5n So we have: 2n - 1.5n = 59 Solve for [I]n[/I] in the equation 2n - 1.5n = 59 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 - 1.5)n = 0.5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.5n = + 59 [SIZE=5][B]Step 3: Divide each side of the equation by 0.5[/B][/SIZE] 0.5n/0.5 = 59/0.5 n = [B]118[/B]

2n - 7 = 0 Solve for [I]n[/I] in the equation 2n - 7 = 0 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -7 and 0. To do that, we add 7 to both sides 2n - 7 + 7 = 0 + 7 [SIZE=5][B]Step 2: Cancel 7 on the left side:[/B][/SIZE] 2n = 7 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 7/2 n = [B]3.5[/B]

2n = 4n Solve for [I]n[/I] in the equation 2n = 4n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 4n. To do that, we subtract 4n from both sides 2n - 4n = 4n - 4n [SIZE=5][B]Step 2: Cancel 4n on the right side:[/B][/SIZE] -2n = 0 [SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = 0/-2 n = [B]0[/B]

2x - b/y = 4c for y Subtract 2x from each side: 2x - 2x - b/y = 4c - 2x Cancel the 2x's on the left side and we get: -b/y = 4c - 2x Cross multiply: -b = y(4c - 2x) Divide each side by (4c - 2x): -b/(4c - 2x) = y(4c - 2x)/(4c - 2x) Cancel the (4c - 2x) on the right side and we get: [B]y = -b/(4c - 2x) [/B]

2x/5 - 9y = 6 for x Add 9y to each side to isolate the x term: 2x/5 - 9y + 9y = 9y + 6 Cancel the 9y's on the left side: 2x/5 = 9y + 6 Multiply each side by 5: 2x * 5/5 = 5(9y + 6) Cancel the 5's on the left side and we get: 2x = 5(9y + 6) Divide each side by 2 to isolate x: 2x/2 = 5/2(9y + 6) Cancel the 2's on the left side and we get our final literal equation of: x = [B]5/2(9y + 6)[/B]

2x/5 - 9y = 6 for x Add 9y to each side of the equation: 2x/5 - 9y + 9y = 6 + 9y Cancel the 9y's on the left side to get: 2x/5 = 6 + 9y Multiply each side of the equation by 5: 5(2x/5) = 5(6 + 9y) Cancel the 5's on the left side to get 2x = 5(6 + 9y) Divide each side of the equation by 2: 2x/2 = 5/2(6 + 9y) Cancel the 2's on the left side to get: x = [B]5/2(6 + 9y)[/B]

2y divided by the sum of 3x and 5 The sum of 3x and 5 means we add 5 to 3x: 3x + 5 2y divided by the sum of 3x and 5: [B]2y/(3x + 5)[/B]

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted 35m. This pattern continues to the end of the track. What percentage of the park did each child paint? 70 + 15 + 35 = 120 When we take[URL='https://www.mathcelebrity.com/modulus.php?num=5000mod120&pl=Calculate+Modulus'] 5000 divided by 120[/URL], we get: 41 remainder 80 So we have: [LIST] [*]Alex: 70 * 41 = 2870 [*]Dell: 15 * 41 = 615 [*]Tony: 35 * 41 = 1435 [/LIST] Now Alex goes next, and paints the full 70. So he has: 2870 + 70 = 2940 Dell goes next, and paints the last 10 615 + 10 = 625 Now for percentages: [LIST] [*]Alex: 2940/5000 = [B]58.8%[/B] [*]Dell: 625/5000 = [B]12.5%[/B] [*]Tony: 1435/5000 = [B]28.7%[/B] [/LIST]

3 quarts of oil is $6.99 how much is one quart of oil? $6.99 / 3 quarts Divide top and bottom by 3: [B]$2.33 / 1 quart[/B]

3/4 a number b divided by 5 3/4 a number b: 3b/4 Divided by 5: 3b/4/5 We multiply top and bottom by 5 to remove the double fraction: 3b*5/4 [B]15b/4[/B]

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as possible where the number of groups of girls and the number of groups of boys is the same .how many boys and how many girls were in each group We want a number such that our total members divided by this number equals our group size. We take the greatest common factor (32,52) = 4 Therefore, we have: [LIST] [*][B]32/4 = 8 girls in each group[/B] [*][B]52/4 = 13 boys in each group[/B] [/LIST]

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE? Set up a proportion in pages to cm: 36 pages /3/8cm = 1 page/x cm Cross multiply: 36x = 3/8 Divide each side by 36 x = 3/(8 * 36) x = 1/(8*12) x = [B]1/96 cm[/B]

3f,subtract g from the result, then divide what you have by h Take this algebraic expression in pieces: 3f subtract g means we subtract the variable g from the expression 3f: 3f - g Divide what we have by h, means we take the result above, 3f - g, and divide it by h: [B](3f - g)/h[/B]

3k^3 = rt for t This is a literal equation. Let's divide each side of the equation by r, to isolate t: 3k^3/r = rt/r Cancel the r's on the right side, and we get: t = [B]3k^3/r[/B]

3n/5 = 1 Cross multiply: 3n = 5 * 1 3n = 5 Divide each side by 3: 3n/3 = 5/3 n = 5/3

4 divided by sin60 degrees. We can write as 4/sin(60). [URL='https://www.mathcelebrity.com/anglebasic.php?entry=60&coff=&pl=sin']Using our trigonometry calculator[/URL], we see sin(60) = sqrt(3)/2. So we have 4/sqrt(3)/2. Multiplying by the reciprocal we have: 4*2/sqrt(3) [B]8/sqrt(3)[/B]

4d/a - 9 = g for a Add 9 to each side: 4d/a - 9 + 9 = g + 9 Cancel the 9's on the left side and we get: 4d/a = g + 9 Cross multiply: 4d = a(g + 9) Divide each side of the equation by (g + 9) to isolate a: 4d/(g + 9) = a(g + 9)/(g + 9) Cancel the (g + 9) on the right side, and we get: a = [B]4d/(g + 9)[/B]

4n - 8 = n + 1 Solve for [I]n[/I] in the equation 4n - 8 = n + 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4n and n. To do that, we subtract n from both sides 4n - 8 - n = n + 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] 3n - 8 = 1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -8 and 1. To do that, we add 8 to both sides 3n - 8 + 8 = 1 + 8 [SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE] 3n = 9 [SIZE=5][B]Step 5: Divide each side of the equation by 3[/B][/SIZE] 3n/3 = 9/3 n = [B]3[/B]

Subtract 5 from each side: -8|-2n| = -80 Divide each side by -8 |-2n| = 10 Since this is an absolute value equation, we need to setup two equations: -2n = 10 -2n = -10 Solving for the first one by dividing each side by -2, we get: n = -5 Solving for the second one by dividing each side by -2, we get: n = 5

5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags Let the cost of each book be b and the cost of each bag be c. We're given 5b + 5c = 175 We can factor this as: 5(b + c) = 175 Divide each side of the equation by 5, we get: (b + c) = 35 The problem asks for 2b + 2c Factor out 2: 2(b + c) we know from above that (b + c) = 35, so we substitute: 2(35) [B]70[/B]

5 girls share 4 sandwiches. What fraction of the sandwich does each girl get? We want to know sandwiches per girls. So we divide: 4 sandwiches per 5 girls [B]4/5[/B]

5 more than the reciprocal of a number Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The reciprocal of this number means we divide 1 over x: 1/x 5 more means we add 5 to 1/x [B]1/x + 5[/B]

5 times a number increased by 4 is divided by 6 times the same number Take this algebraic expression in parts. Part 1: 5 times a number increased by 4 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x [*]5 times the number means multiply x by 5: 5x [*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4 [/LIST] Part 2: 6 times the same number [LIST] [*]From above, [I]a number[/I] is x: x [*]6 times the number means we multiply x by 6: 6x [/LIST] The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator. [B](5x + 4)/6x[/B]

5 times x 5x Divided by 7 5x/7

5 times y 5y Divided by 8 5y/8

5n - 5 = 85 Solve for [I]n[/I] in the equation 5n - 5 = 85 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -5 and 85. To do that, we add 5 to both sides 5n - 5 + 5 = 85 + 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 5n = 90 [SIZE=5][B]Step 3: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 90/5 n = [B]18[/B]

6 is divided by square of a number The phrase [I]a number [/I]means an arbitrary variable, let's call it x. x the square of this means we raise x to the power of 2: x^2 Next, we divide 6 by x^2: [B]6/x^2[/B]

6 times a number multiplied by 3 all divided by 4 Take this algebraic expression in parts: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]6 times a number: 6x [*]Multiplied by 3: 3(6x) = 18x [*]All divided by 4: 18x/4 [/LIST] We can simplify this: We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is: [B]9x/2[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 . This is an algebraic expression. Let's take it in parts: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The reciprocal of a number x means we divide 1 over x: 1/x 6 times the reciprocal means we multiply 6 by 1/x: 6/x The reciprocal of 7 means we divide 1/7 1/7 3 times the reciprocal means we multiply 1/7 by 3: 3/7 Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7 [B]6/x = 3/7[/B] <-- This is our algebraic expression If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get: x = 14

6 times the sum of a number and 5 is 16 A number represents an arbitrary variable, let's call it x x The sum of x and 5 x + 5 6 times the sum of x and 5 6(x + 5) Is means equal to, so set 6(x + 5) equal to 16 [B]6(x + 5) = 16 <-- This is our algebraic expression Solve for x[/B] Multiply through: 6x + 30 = 16 Subtract 30 from each side: 6x - 30 + 30 = 16 - 30 6x = -14 Divide each side by 6 6x/6 = -14/6 Simplify this fraction by dividing top and bottom by 2: x = [B]-7/3 [MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]

6 times y divided by x squared 6 times y: 6y x squared means we raise x to the power of 2: x^2 The phrase [I]divided by[/I] means we have a fraction: [B]6y/x^2[/B]

6 times y divided by x squared 6 times y: 6y x squared means we raise x to the power of 2: x^2 The phrase [I]divided by[/I] means we divide 6y by x^2: [B]6y/x^2[/B]

64 divided by the cube of y The cube of y means y raised to the 3rd power: y^3 64 divided by this: [B]64/y^3[/B]

69 divided by the sum of 10 and y The sum of 10 and y 10 + y 69 divided by this [B]69/(10 + y)[/B]

7 minus a number all divided by 4 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 7 minus a number 7 - x All divided by 4: [B](7 - x)/4[/B]

7n + 4 + n - 5 = 63 Solve for [I]n[/I] in the equation 7n + 4 + n - 5 = 63 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (7 + 1)n = 8n [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 4 - 5 = -1 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 8n - 1 = + 63 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants -1 and 63. To do that, we add 1 to both sides 8n - 1 + 1 = 63 + 1 [SIZE=5][B]Step 5: Cancel 1 on the left side:[/B][/SIZE] 8n = 64 [SIZE=5][B]Step 6: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 64/8 n = [B]8[/B]

8 sweets divided by 4 pupils = 2 sweets per pupil. We can also write this as a proportion: 8 sweets x sweets ---------- = ------------ 4 pupils 1 pupil Express this as 8/4 = x/1. [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=x&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Enter that into the search engine[/URL] x = 2

8 to the power of 8 divided by 8 8 to the power of 8 8^8 Divided by 8 [B]8^8/8[/B]

8 to the power of x over 2 to the power of y Step 1: 8 to the power of x means we take 8 and raise it to an exponent of x: 8^x Step 2: 2 to the power of y means we take 2 and raise it to an exponent of y: 2^y Step 3: The word [I]over[/I] means a quotient, also known as divided by, so we have: [B]8^x/2^y [MEDIA=youtube]SPQKOt5EoqA[/MEDIA][/B]

85 bags of nuts are to be divided among 18 friends. Each bag contains 15 nuts. How many nuts will each friend get? [B][U]Calculate the total nuts:[/U][/B] Total Nuts = Total Bags * Nuts Per Bag Total Nuts = 85 * 15 Total Nuts = 1,275 [B][U]Figure out how many nuts each person gets:[/U][/B] Nuts per person = Total Nuts / Friends Nuts per person = 1,275 / 18 Nuts per person = [B]70.83[/B]

9 divided by the quantity x plus y The quantity x plus y: x + y 9 divided by this quantity: [B]9/(x + y)[/B]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4. Build our two algebraic expressions first: 9 divided by the sum of x and 4 9/(x + 4) 6 divided by x minus 4 6/(x - 4) The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other: [B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, we cross multiply: 9(x - 4) = 6(x + 4) To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]20[/B]

9 rulers cost the same as 11 erasers. One eraser cost 0.09 cents. What is the cost of 1 ruler Let the cost of a ruler be r. We're given: 9r = 11(0.09) 9r = 0.99 Divide each side by 9 and we get: r = [B]0.11[/B]

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain? Let c equal the number of crates 9 bottles per crate * c = 993 9c = 993 Solve for [I]c[/I] in the equation 9c = 993 [SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE] 9c /9 = 993/9 c = 110.33333333333 Since we can't have fractional crates, we round up 1 to the next full crate c = [B]111[/B]

A 128 ounce carton of milk states that there are 20 servings. How many ounces are in a serving? We divide 128 ounces by 20 servings to get ounces per serving: 128 ounces / 20 servings [B]6.4 ounces / serving[/B]

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of aluminum Divide 24 by 2.5 to get number of sheets: 24/2.5 = 9.6 So we have 9 full sheets. Which means each strip is [B]0.6 wide[/B]

A 3 gallon bottle of bleach cost $16.32. What is the price per cup? We're given 16.32 / 3 gallons Divide the top and bottom of the fraction by 3 to get the cost per gallon: 16.32/3 = 5.44 gallon Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']measurement converter[/URL], we see that: 1 gallon = 16 cups So 5.44 /16 cups=[B]$0.34 per cup[/B]

A 3-gallon bucket of paint costs $87.12. What is the price per quart? 3 gallons equals 12 quarts with our [URL='https://www.mathcelebrity.com/liqm.php?quant=3&pl=Calculate&type=gallon#quart']conversion calculator[/URL]. We divide 87.12 for 12 quarts by 12: [URL='https://www.mathcelebrity.com/perc.php?num=87.12&den=12&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']87.12 / 12[/URL] = [B]$7.26 per quart[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800? Let x be the number of $24 tickets, and y be the number of $40 tickets. We have: [LIST=1] [*]24x + 40y = 188,800 [*]x + y = 6,000 [*]Rearrange (2) to solve for x: x = 6000 - y [*]Plug in (3) to (1): [/LIST] 24(6000 - y) + 40y = 188800 144,000 - 24y + 40y = 188,800 16y + 144,000 = 188,800 Subtract 144,000 from each side: 16y = 44,800 Divide each side by 16 y = 2,800 ($40 tickets) Plug this into (2) x + 2,800 = 6000 Subtract 2,800 from each side: x = 3,200 ($24 tickets)

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch? Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that: 7 feet = 84 inches So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch: $3.36/84 = [B]0.04 per inch[/B]

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be? The key phrase in this problem is [B]two pieces[/B]. Declare Variables: [LIST] [*]Let the short piece length be s [*]Let the long piece length be l [/LIST] We're given the following [LIST=1] [*]s = l - 10 [*]s + l = 98 (Because the two pieces add up to 98) [/LIST] Substitute equation (1) into equation (2) for s: l - 10+ l = 98 Group like terms: 2l - 10 = 98 Solve for [I]l[/I] in the equation 2l - 10 = 98 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 98. To do that, we add 10 to both sides 2l - 10 + 10 = 98 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 2l = 108 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2l/2 = 108/2 l = [B]54[/B] To solve for s, we substitute l = 54 into equation (1): s = 54 - 10 s = [B]44[/B] Check our work: The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10 Second check: Do both pieces add up to 98 54 + 44 ? 98 98 = 98

a = v^2/r for r Start by cross multiplying to get r out of the denominator: ar = v^2 Divide each side of the equation by a to isolate r: ar/a = v^2/a Cancel the a's on the left side, and we get: r = [B]v^2/a[/B]

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn? [LIST] [*]Let the number of ducks be d. Duck legs = 2 * d = 2d [*]Number of cows = 2d. Cow legs = 4 * 2d = 8d [*]1 dog Tripod has 3 legs [/LIST] Total legs: 2d + 8d + 3 = 313 Solve for [I]d[/I] in the equation 2d + 8d + 3 = 313 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (2 + 8)d = 10d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 10d + 3 = + 313 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 313. To do that, we subtract 3 from both sides 10d + 3 - 3 = 313 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 10d = 310 [SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE] 10d/10 = 310/10 d = [B]31[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=2d%2B8d%2B3%3D313&pl=Solve']Source[/URL]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ? 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ? 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ? 252.4.5 [B]t ? 56[/B]

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equation to describe this relationship We know the distance (d) equation in terms of rate (r) and time (t) as: d = rt We're given d = 336km and t = 12 hours, so we have: [B]336 km = 12t [/B] <-- this is our equation Divide each side by 12 to solve for t: 12t/12 = 336/12 t = [B]28 km / hour[/B]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each. [B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B] C(b) = Fixed Cost + Variable Cost x Number of Units C(b) = 180,000 + 25(b) [B]Set up Revenue Function R(b):[/B] R(b) = 40b Set them equal to each other 180,000 + 25b = 40b Subtract 25b from each side: 15b = 180,000 Divide each side by 15 [B]b = 12,000 for break even[/B]

A cake is to be divided into 8 equal parts. After division, each equal portion is again divided into 2 equal individual parts. How big is each of the new equal parts? 1 cake * 8 parts * 2 parts = 16 parts. So each slice is 1/16 of a cake.

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. Set up the depreciation equation D(t) where t is the number of years in the life of the car: D(t) = 24,000 * (1 - 0.3)^t D(t) = 24000 * (0.7)^t The problem asks for D(t)<=7300 24000 * (0.7)^t = 7300 Divide each side by 24000 (0.7)^t = 7300/24000 (0.7)^t= 0.30416666666 Take the natural log of both sides: LN(0.7^t) = -1.190179482215518 Using the natural log identities, we have: t * LN(0.7) = -1.190179482215518 t * -0.35667494393873245= -1.190179482215518 Divide each side by -0.35667494393873245 t = 3.33687437943 [B]Rounding this up, we have t = 4[/B]

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly rate I was charge for labor Subtract the cost of parts from the total repair bill to get the labor cost: Labor Cost = Total Bill - Parts Cost Labor Cost = 441 - 153 Labor Cost = 288 Labor Cost can be broken down into Labor divided by hours Hourly Labor Rate = Labor Cost / Labor Hours Hourly Labor Rate = = 288 / 4 Hourly Labor Rate = [B]72[/B]

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same? Let g be the number of GB. The limited plan has a cost as follows: C = 10(g - 5) + 55 C = 10g - 50 + 55 C = 10g + 5 We want to set the limited plan equal to the unlimited plan and solve for g: 10g + 5 = 70 Solve for [I]g[/I] in the equation 10g + 5 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 5 and 70. To do that, we subtract 5 from both sides 10g + 5 - 5 = 70 - 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 10g = 65 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10g/10 = 65/10 g = [B]6.5[/B] Check our work for g = 6.5: 10(6.5) + 5 65 + 5 70

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour. Let h be the number of hours. We have the equation: 3 * (1.1)^h = 1,200 Divide each side by 3: 1.1^h = 400 [URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h: h = 62.86 To the nearest hour, we round up and get [B]h = 63[/B]

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public transportation, 1/9 cycle, and the remainder use other methods of transportation. How many employees use each method of transportation? Find the remainder fraction: Remainder = 1 - (1/4 + 1/6 + 1/8 + 1/9) The least common multiple of 4, 6, 8, 9 is 72. So we divide 72 by each fraction denominator to get our multiplier: 1/4 = 18/72 1/6 = 12/72 1/8 = 9/72 1/9 = 8/72 Add those all up: (18 + 12 + 9 + 8)/72 47/72 Now subtract the other methods out from 1 to get the remainder of who use other methods: Remainder = 1 - 47/72 Since 1 = 72/72, we have: (72 - 47)/72 [B]25/72[/B]

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per year through retirements, until its total employment is 2560. How long will this take? Figure out how many reductions are needed 4900 - 2560 = 2340 We want 300 per year for retirements, so let x equal how many years we need to get 2340 reductions. 300x = 2340 Divide each side by 300 x = 7.8 years. If we want full years, we would do 8 full years

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them? Let w = weeks 7 kilometers per week * w = 43.75 To solve for w, we divide each side of the equation by 7: 7w/7 = 43.75/7 Cancel the 7's, we get: w = [B]6.25 [/B]

A construction worker can lift 220 lb, while an architect can only lift 40 lb. The construction worker can lift how many times what the architect can lift? [URL='https://www.mathcelebrity.com/perc.php?num=220&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']We divide 220 by 40 to get the multiplier:[/URL] 220/40 = [B]5.5 times[/B]

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be? Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations: [LIST=1] [*]f = 10s [*]s + f = 8 & 1/4 [/LIST] Substitute (1) into (2): s + 10s = 8 & 1/4 11fs= 33/4 <-- 8 & 1/4 = 33/4 Cross multiply: 44s = 33 Divide each side by 44: s= 33/44 Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B] Now substitute this into (1): f = 10(33/44) [B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for getting a D on a math test and he gave another son an extra $35 for doing extra chores. Combined, the sons had $81. Figure out how much each son had. Let x, y, and z be the money each son received. To begin, x = y = z. But then, Dad took 20 from son X and gave it to son Y. So now, x = y - 20 Next, he gave Son Z an extra $35 for chores So z is now y + 35 since y and z used to be equal Combined, they all have 81. x + y + z = 181 But with the changes, it is: (y - 20) + y + (y + 35) Combine like terms: 3y - 20 + 35 = 81 3y + 15 = 81 Subtract 15 from each side: 3y = 66 Divide each side by 3 to isolate y y = 22 Since x = y - 20, x = 2 Since z = y + 35, we have z = 57 Checking our work, 2 + 22 + 57 = 81.

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green? We are drawing without replacement. Take each draw probability: [LIST=1] [*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25 [*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24 [/LIST] Since both events are independent, we have: P(Green) * P(Green) = 8/25 * 7/24 P(Green) * P(Green) = 56/600 Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8. [B]P(Green) * P(Green) = 7/75[/B]

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers somethings from various ways she tried packing the eggs. When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over. What can the farmer figure from this information about the number of eggs she had? Is there more than one answer? We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7. 217 + 84 = [B]301[/B]. Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.

A father is K years old and his son is M years younger. The sum of their ages is 53. Father's Age = K Son's Age = K - M and we know K + (K - M) = 53 Combine like terms: 2K - M = 53 Add M to each side: 2K - M + M = 53 + M Cancel the M's on the left side, we get: 2K = 53+ M Divide each side by 2: 2K/2 = (53 + M)/2 Cancel the 2's on the left side: K = [B](53 + M)/2[/B]

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1,500 companies listed on the exchange, how many are of interest of her? First, use our [URL='http://www.mathcelebrity.com/zscore.php?z=p%280.14%3Cz%3C0.16%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(0.14 < z < 0.16) = 0.007889 Divide that by 2 for two-tail test to get0.003944729 Use the NORMSINV(0.003944729) in Excel to get the Z value of 2.66 Therefore, the companies of interest are 2.66 * 1500 * 0.10 = [B]399[/B]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 6 [*]2x + y = 15 [/LIST] Multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -12 [*]2x + y = 15 [/LIST] Now add them -2x + 2x - 4y + y = -12 + 15 -3y = 3 Divide each side by -3: y = 3/-3 y =[B] -1[/B] Plug this back into equation 1: x + 2(-1) = 6 x - 2 = 6 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]8[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers Let the first number be a and the second number be b. We have: [LIST=1] [*]a + 2b = 7 [*]2a + b = 23 [/LIST] Rearrange (1) into (3) (3) a = 7 - 2b Substitute (3) into (2): 2(7 - 2b) + b = 23 Multiply through: 14 - 4b + b = 23 Combine like terms: 14 - 3b = 23 Subtract 14 from each side: -3b = 9 Divide each side by -3 [B]b = -3[/B] Substitute this into (3) a = 7 - 2b a = 7 - 2(-3) a = 7 + 6 [B]a = 13[/B] [B](a, b) = (13, -3)[/B]

A football gained 52 yards during the possession. In the next 3 possessions they gained the same amount of yards each time. If they gained a total of 256 yards, write and solve an equation for how many yards they gained in each of the last 3 possessions. Subtract 52 initial yards 256 - 52 = 204 Now, divide 204 by 3 possessions 204/3 = [B]68 yards[/B]

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction. Let the fraction be x/y. We're given two equations: [LIST=1] [*]x/y = 3/4 [*](x + 7)/y = 4/3. [I](The reciprocal of 3/4 is found by 1/(3/4)[/I] [/LIST] Cross multiply equation 1 and equation 2: [LIST=1] [*]4x = 3y [*]3(x + 7) = 4y [/LIST] Simplifying, we get: [LIST=1] [*]4x = 3y [*]3x + 21 = 4y [/LIST] If we divide equation 1 by 4, we get: [LIST=1] [*]x = 3y/4 [*]3x + 21 = 4y [/LIST] Substitute equation (1) into equation (2) for x: 3(3y/4) + 21 = 4y 9y/4 + 21 = 4y Multiply the equation by 4 on both sides to eliminate the denominator: 9y + 84 = 16y To solve this equation for y, we type it in our math engine and we get: y = [B]12 [/B] We then substitute y = 12 into equation 1 above: x = 3 * 12/4 x = 36/4 x = [B]9 [/B] So our original fraction x/y = [B]9/12[/B]

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes? n gallons / t hours = n/t gallons per hour are leaking The value of the gas that leaks each hour is $2, so we have: 2n/t dollar per hour is leaking Value per minute means we divide by 60: 2n/60t Dividing top and bottom by 2 to simplify, we have: n/30t Given m minutes, we multiply to get: [B]nm/30t[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots? We want the probability a student from your school is chosen out of total students times total ways to choose students from your school: [U]a) P(5 students being selected):[/U] 5/30 * 4/(120 - 30) 5/30 * 4/90 20/2700 [URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get: 1/135 [U]b) Total Ways 9 students can be picked from your school:[/U] 9/120 [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get: 3/40 Divide a by b: 1/135 / 3/40 40/405 [URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get: [B]8/81[/B]

A gym has 18 exercise stations, including 2 rowing machines. What is the probability that a randomly selected exercise station will be a rowing machine? The probability is 2/18. We can simplify this fraction. Divide top and bottom by 2: [B]1/9[/B]

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute 3206 full turns / 7 minutes [URL='https://www.mathcelebrity.com/fraction.php?frac1=3206%2F7&frac2=3%2F8&pl=Simplify']Divide the fraction by 7 to get turns per minute[/URL] [B]458 turns per minute[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it�s starting point? The distance forms a right triangle. We want the distance of the hypotenuse. Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B]. We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot? [U]Set up equations:[/U] (1) 2l + 2w = 800 (2) l = 3w - 20 [U]Substitute (2) into (1)[/U] 2(3w - 20) + 2w = 800 6w - 40 + 2w = 800 [U]Group the w terms[/U] 8w - 40 = 800 [U]Add 40 to each side[/U] 8w = 840 [U]Divide each side by 8[/U] [B]w = 105 [/B] [U]Substitute w = 105 into (2)[/U] l = 3(105) - 20 l = 315 - 20 [B]l = 295[/B]

A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each. Let the house cost be h, and the lot cost be l. We have the following equations: [LIST=1] [*]h = 3.5l [*]h + l = 135,000 [/LIST] Substitute (1) into (2) 3.5l + l = 135,000 Combine like terms: 4.5l = 135,000 Divide each side by 4.5 to isolate l [B]l = 30,000[/B] Substitute this back into equation (1) h = 3.5(30,000) [B]h = 105,000[/B]

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes? Use the formula D = rt where [LIST] [*]D = distance [*]r = rate [*]t = time [/LIST] The plan traveling 150 mph for 3 hours: Time 1 = 150 Time 2 = 300 Time 3 = 450 Now at Time 3, the other plane starts Time 4 = 600 Time 5 = 750 Time 6 = 450 + 150t = 550t Subtract 150t 400t = 450 Divide each side by 400 t = 1.125 Plug this into either distance equation, and we get: 550(1.125) = [B]618.75 miles[/B]

a landscaper buys 1 gallon of plant fertilizer. he uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. how many gallons does he put into each bottle? First, we find the remaining fraction of fertilizer after using 1/5. [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F5&pl=Subtract']Using our fraction calculator[/URL], we see: 1 - 1/5 = 4/5 To find the amount of fertilizer per bottle, we then [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F5&frac2=3&pl=Divide']divide 4/5 by 3 and we get[/URL]: [B]4/15 gallon per bottle[/B]

A laundry basket contains 30 socks, of which 9 are black. What is the probability that a randomly selected sock will be black? P(Black) = 9/30 Simplifying, we can divide top and bottom by 3: [B]3/10 3/10 as a percentage is 30%[/B]

A local Dunkin� Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year�s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago? Declare variable and convert numbers: [LIST] [*]16% = 0.16 [*]let the sales 2 years ago be s. [/LIST] s(1 + 0.16)(1 + 0.16) = 80,642 s(1.16)(1.16) = 80,642 1.3456s = 80642 Solve for [I]s[/I] in the equation 1.3456s = 80642 [SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE] 1.3456s/1.3456 = 80642/1.3456 s = 59930.142687277 s = [B]59,930.14[/B]

A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How many hamburgers were sold? Let h = number of hamburgers sold and c be the number of cheeseburgers sold. We have two equations: (1) c = h - 51 (2) c + h = 499 Substitute (1) into (2) h - 51 + h = 499 Combine like terms 2h - 51 = 499 Add 51 to both sides 2h = 550 Divide each side by 2 to isolate h [B]h = 275[/B]

A man left a warehouse at 9:00 a.m. and travels 150 km to reach his home. What is the speed if he arrives at 11:00 a.m.? [LIST] [*]His trip took 2 hours (11 - 9) [*]He traveled 150 km in 2 hours [*]His speed is measured in km per hour [/LIST] If we have 150km/2 hours, we want his speed in km per hour Divide top and bottom by 2 [B]75km/hr[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47? Subtract the join fee from the total cost: $47 - $16 = $31 Now divide this number by the cost per event: $31 / $1 = [B]31 events[/B]

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? [U]Assumptions:[/U] [LIST] [*]B = the speed of the boat in still water. [*]S = the speed of the stream [/LIST] Relative to the bank, the speeds are: [LIST] [*]Upstream is B - S. [*]Downstream is B + S. [/LIST] [U]Use the Distance equation: Rate * Time = Distance[/U] [LIST] [*]Upstream: (B-S)6 = 258 [*]Downstream: (B+S)6 = 330 [/LIST] Simplify first by dividing each equation by 6: [LIST] [*]B - S = 43 [*]B + S = 55 [/LIST] Solve this system of equations by elimination. Add the two equations together: (B + B) + (S - S) = 43 + 55 Cancelling the S's, we get: 2B = 98 Divide each side by 2: [B]B = 49 mi/hr[/B] Substitute this into either equation and solve for S. B + S = 55 49 + S = 55 To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get: S = [B]6 mi/hr[/B]

A number multiplied by 6 and divided by 5 give four more than a number? A number is represented by an arbitrary variable, let's call it x. Multiply by 6: 6x Divide by 5 6x/5 The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4. 6x/5 = x + 4 Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side: 6x(5)/5 = 5(x + 4) The 5's cancel on the left side, giving us: 6x = 5x + 20 Subtract 5x from each side [B]x = 20[/B] Check our work from our original equation: 6x/5 = x + 4 6(20)/5 ? 20 + 4 120/5 ?24 24 = 24 <-- Yes, we verified our answer

a number of pennies splits into 4 equal groups The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take x and divide it by 4 to get 4 equal groups: [B]x/4[/B]

A parking garage charges $5 plus $2 per hour. You have $16 to spend for parking. How many hours can you park? Subtract the flat rate to get the amount you have for hourly parking: 16 - 5 = 11 So we divide 11 dollars to park by 2 dollars per hour to get: 11/2 [B]5.5 hours[/B]

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there? Let d = the number of dimes and q = the number of quarters. We have two equations: (1) d + q = 146 (2) 0.1d + 0.25q = 27.05 Rearrange (1) into (3) solving for d (3) d = 146 - q Substitute (3) into (2) 0.1(146 - q) + 0.25q = 27.05 14.6 - 0.1q + 0.25q = 27.05 Combine q's 0.15q + 14.6 = 27.05 Subtract 14.6 from each side 0.15q = 12.45 Divide each side by 0.15 [B]q = 83[/B] Plugging that into (3), we have: d = 146 - 83 [B]d = 63[/B]

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at station B at 10:00 p.m. A transit train left from station A 1 hour later than the passenger train, but it arrived at the station B at the same time with the passenger train. What was the average speed of the transit train? [U]Passenger Train[/U] [LIST] [*]45 miles per hour and it got there in 4 hours. [/LIST] Using our formula D = rt where: [LIST] [*]D = Distance [*]r = rate [*]t = time [/LIST] [LIST] [*]D = rt [*]D = 45(4) [*]D = 180 miles from Station A to Station B [/LIST] Transit Train [LIST] [*]It has to go the same distance, 180 miles, so D = 180 [*]It made it there in 3 hours. This is r [*]We want to solve for t [/LIST] D = rt 180 = 3r Divide each side by 3 [B]r = 60 miles per hour[/B]

A penny has a diameter of 19 millimeters. What is the radius of the penny. D = 2r To solve for r, we divide each side by 2: r = D/2 Plugging in D = 19, we get: r = [B]19/2 or 9.5[/B]

a piece of ribbon is y cm long. Ashley cut it into 4 equal pieces to do her 4 sisters hair. write an expression for the amount of ribbon used for each sister We take y cm and divide it equal among 4 sisters: [B]y/4[/B]

A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there? Let h be the number of half-dollars and q be the number of quarters. Set up two equations: (1) q = h + 2 (2) 0.25q + 0.5h = 11.75 [U]Substitute (1) into (2)[/U] 0.25(h + 2) + 0.5h = 11.75 0.25h + 0.5 + 0.5h = 11.75 [U]Group h terms[/U] 0.75h + 0.5 = 11.75 [U]Subtract 0.5 from each side[/U] 0.75h = 11.25 [U]Divide each side by h[/U] [B]h = 15[/B] [U]Substitute h = 15 into (1)[/U] q = 15 + 2 [B]q = 17[/B]

A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to solve for t, we get: t = [B]18.85 years[/B] Note: if you need an integer answer, we round up to 19 years

A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the speed of the commercial jet was 154 mph less than 3 times the speed of the private jet, find the speed of each jet. Let p = private jet speed and c = commercial jet speed. We have two equations: (1) c = 3p - 154 (2) 4p =2c Plug (1) into (2): 4p = 2(3p - 154) 4p = 6p - 308 Subtract 4p from each side: 2p - 308 = 0 Add 308 to each side: 2p = 308 Divide each side by 2: [B]p = 154[/B] Substitute this into (1) c = 3(154) - 154 c = 462 - 154 [B]c = 308[/B]

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $67000, what was the amount of her sales? Total post-salary pay = $67,000 - $25,000 = $42,000 Let Sales be s. So 0.03s = $42,000 Divide each side by 0.03 s = $1,400,000

a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are needed for 30 bread rolls? Set up a proportion of bread rolls per tablespoons of butter where t is the amount of tablespoons of butter needed for 30 bread rolls: 20/5 = 30/t Cross multiply our proportion: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 20t = 30 * 5 20t = 150 Divide each side of the equation by 20: 20t/20 = 150/20 Cancel the 20's on the left side and we get: t = [B]7.5[/B]

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions? We know the rectangle has the following formulas: Area = lw Perimeter = 2l + 2w Given an area of 238 and a perimeter of 62, we have: [LIST=1] [*]lw = 238 [*]2(l + w) = 62 [/LIST] Divide each side of (1) by w: l = 238/w Substitute this into (2): 2(238/w + w) = 62 Divide each side by 2: 238/w + w = 31 Multiply each side by w: 238w/w + w^2 = 31w Simplify: 238 + w^2 = 31w Subtract 31w from each side: w^2 - 31w + 238 = 0 We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get: w = (14, 17) We take the lower amount as our width and the higher amount as our length: [B]w = 14 l = 17 [/B] Check our work for Area: 14(17) = 238 <-- Check Check our work for Perimeter: 2(17 + 14) ? 62 2(31) ? 62 62 = 62 <-- Check

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions? We are given or know the following about the rectangle [LIST] [*]l = 2w [*]P = 2l + 2w [*]Since P = 360, we have 2l + 2w = 360 [/LIST] Since l = 2w, we have 2l + (l) = 360 3l = 360 Divide by 3, we get [B]l = 120[/B] Which means w = 120/2 [B]w = 60[/B]

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have: (1073 + 1108 + s)/3 = 1000 Cross multiply: 1073 + 1108 + s = 1000 * 3 1073 + 1108 + s = 3000 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]819[/B]

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds? For simple interest, we have: Balance * interest rate = Interest payment 8000i = 584 Divide each side of the equation by 8000 to isolate i: 8000i/8000 = 584/8000 Cancelling the 8000's on the left side, we get: i = 0.073 Most times, interest rates are expressed as a percentage. Percentage interest = Decimal interest * 100% Percentage interest = 0.073 * 100% Multiplying by 100 is the same as moving the decimal point two places right: Percentage interest = [B]7.3%[/B]

A Salesperson receives a weekly salary of $100 plus a 5.5% commission on sales. Her salary last week was $1090. What were her sales that week? $1,090 - 100 = $990. This is her commission. Let s = Sales. So 0.055s = $990 Divide each side by 0.055. s = $18,000

A section of land measuring 3 & 3/6 acres is divided equally among 7 people. How many acres will each person get? We want 3&3/6 /7 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%263%2F6&frac2=7&pl=Divide']Using our fraction calculator[/URL], we get: [B]1/2 acre per person[/B]

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes? Let d be the number of days: Daily Plan cost: 75d + 20d = 95d Season Pass: 350 + 20d We want to find d such that 350 + 20d < 95d Subtract 20d from each side 75d > 350 Divide each side by 75 d > 4.66667 [B]d = 5[/B]

A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second? 144 feet/3 seconds Divide top and bottom by 3 to get feet per second [B]48 feet per second[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age. Declare variables: [LIST] [*]Let f be the father's age [*]Let s be the son's age [/LIST] We're given two equations: [LIST=1] [*]s = f/4 [*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I] [/LIST] Using substitution, we substitute equaiton (1) into equation (2) for s: f - f/4 = 30 To remove the denominator/fraction, we multiply both sides of the equation by 4: 4f - 4f/4 = 30 *4 4f - f = 120 3f = 120 To solve for f, we divide each side of the equation by 3: 3f/3 = 120/3 Cancel the 3's on the left side and we get: f = [B]40[/B]

A spherical water tank holds 11,500ft^3 of water. What is the diameter? The tank holding amount is volume. And the volume of a sphere is: V = (4pir^3)/3 We know that radius is 1/2 of diameter: r =d/2 So we rewrite our volume function: V = 4/3(pi(d/2)^3) We're given V = 11,500 so we have: 4/3(pi(d/2)^3) = 11500 Multiply each side by 3/4 4/3(3/4)(pi(d/2)^3) = 11,500*3/4 Simplify: pi(d/2)^3 = 8625 Since pi = 3.1415926359, we divide each side by pi: (d/2)^3 = 8625/3.1415926359 (d/2)^3 = 2745.42 Take the cube root of each side: d/2 = 14.0224 Multiply through by 2: [B]d = 28.005[/B]

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins? We want Expected Value of s spins. Set up the expected value formula for any number 1-4 E(s) = 0.25 * n where n is the number of spins. Using s = 3, n = 10,000, we have: E(10,000) = 0.25 * 10,000 E(10,000) = [B]2,500[/B]

A stack of boards is 21 inches high. Each board is 1� inches thick. How many boards are there? We want 21 / 1 & 3/4 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=21&frac2=1%263%2F4&pl=Divide']fraction operation calculator[/URL], we get: [B]12 boards[/B]

a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses? The build rate of houses per days is proportional. Set up a proportion of [I]houses to days[/I] where d is the number of days it takes to build 11 houses: 7/3 = 11/d Cross multiply: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 7d = 11 * 3 7d = 33 Divide each side of the equation by 7: 7d/7 = 33/7 d = [B]4.7142857142857[/B]

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minute? 1500 meters / 30 minutes Divide top and bottom by 30 [B]50 meters / minute[/B]

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase? Setup number of coins: [LIST] [*]Number of nickels = n [*]Number of dimes = 2.5n [*]Number of quarters = 5n [/LIST] Setup value of coins: [LIST] [*]Value of nickels = 0.05n [*]Value of dimes = 2.5 * 0.1n = 0.25n [*]Value of quarters = 5 * 0.25n = 1.25n [/LIST] Add them up: 0.05n + 0.25n + 1.25n = 24.80 Solve for [I]n[/I] in the equation 0.05n + 0.25n + 1.25n = 24.80 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (0.05 + 0.25 + 1.25)n = 1.55n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 1.55n = + 24.8 [SIZE=5][B]Step 3: Divide each side of the equation by 1.55[/B][/SIZE] 1.55n/1.55 = 24.80/1.55 n = [B]16[/B] [B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.25n%2B1.25n%3D24.80&pl=Solve']Source[/URL][/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years Simple interest formula if we start with 1 dollar and double to 2 dollars: 1(1 + i(20)) = 2 1 + 20i = 2 Subtract 1 from each side: 20i = 1 Divide each side by 20 i = 0.05 Now setup the same simple interest equation, but instead of 2, we use 3: 1(1 + 0.05(t)) = 3 1 + 0.05t = 3 Subtract 1 from each side: 0.05t = 2 Divide each side by 0.05 [B]t = 40 years[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies? We set up our exponential function where n is the number of days after today: Z(n) = 25 * 2^n We want to know n where Z(n) = 25,000. 25 * 2^n = 25,000 Divide each side of the equation by 25, to isolate 2^n: 25 * 2^n / 25 = 25,000 / 25 The 25's cancel on the left side, so we have: 2^n = 1,000 Take the natural log of each side to isolate n: Ln(2^n) = Ln(1000) There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have: n * Ln(2) = Ln(1,000) 0.69315n = 6.9077 [URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get: [B]n = 9.9657 days ~ 10 days[/B]

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel? Setup an equation where x is the number of miles traveled: 0.65x + 1.75 = 10 Subtract 1.75 from each side: 0.65x = 8.25 Divide each side by 0.65 [B]x = 12.69 miles[/B] If we do full miles, we round down to 12. [MEDIA=youtube]mFqUe2mjX-w[/MEDIA]

A test has 90 questions and you answered 69 correctly. What fraction did you get correct? 69/90 Divide top and bottom by 3 to simplify: [B]23/30[/B]

a textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold? Let h = history book and s = sociology books. We have 2 equations: (1) h = s - 42 (2) h + s = 296 Substitute (1) to (2) s - 42 + s = 296 Combine variables 2s - 42 = 296 Add 42 to each side 2s = 338 Divide each side by 2 s = 169 So h = 169 - 42 = 127

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4 degrees Range = Max - Min Divide this by 2 to get the lesser half and larger half: Half-Range = 1.5/2 Half-Range = 0.75 [U]Our Maximum temperature is:[/U] Max Temp = Current Temp + Half-Range Max Temp = 87.4 + 0.75 Max Temp = [B]88.15 [/B] [U]Our Minimum temperature is:[/U] Min Temp = Current Temp - Half-Range Min Temp = 87.4 - 0.75 Min Temp = [B][B]86.65[/B][/B]

a times b divided by the quantity a minus b a times b: ab a minus b: a - b Now divide a times b by a minus b: [B]ab/(a - b)[/B]

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk? Distance formula (d) for a rate (r) and time (t) is: d = rt We're given d = 12.5 and r = 5 12.5 = 5t 5t = 12.5 Solve for t. Divide each side of the equation by 5: 5t/5 = 12.5/5 Cancel the 5's on left side and we get: t = [B]2.5[/B]

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71 Set up a cost equation C(m) where m is the number of miles: C(m) = Cost per mile * m + Service Fee Plugging in the service fee of 50 and cost per mile of 1.75, we get: C(m) = 1.75m + 50 The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m: 1.75m + 50 = 71 Solve for [I]m[/I] in the equation 1.75m + 50 = 71 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 50 and 71. To do that, we subtract 50 from both sides 1.75m + 50 - 50 = 71 - 50 [SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE] 1.75m = 21 [SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE] 1.75m/1.75 = 21/1.75 m = [B]12[/B]

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid? Setup measurements: [LIST] [*]Small base = n [*]Large base = 1.2n [*]sides = n/2 [*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4 [/LIST] Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1.2 + 0.5 + 0.5)n = 3.2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 3.2n = + 54.4 [SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE] 3.2n/3.2 = 54.4/3.2 n = [B]17[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

A trench is 40 feet long and the trencher goes 2 feet per minute. How long does it take to dig the trench? 2 feet per minute * x minutes = 40 feet Divide each side by 2 [B]x = 20 minutes[/B]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle? First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4. We divide the 3 side lengths by 4: 12/4 = 3 16/4 = 4 20/4 = 5 And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A varies directly as B and inversely as C. There exists a constant k such that: [B]a = kb/c [/B] Inversely means we divide by and directly means we multiply by

a varies directly with b and inversely with c Direct variation means we multiply. Inverse variation means we divide. There exists a constant k such that: [B]a = kb/c[/B]

a varies inversely with b, c and d Varies inversely means we divide. Given a constant, k, we have: [B]a = k/bcd[/B]

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost? Let the cost of the soda be p. So the cost of a hot dog is 2p. The total cost of hot dogs: 2hp The total cost of sodas: ps The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d: 2hp + ps = d We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side: p(2h + s) = d Divide each side of the equation by (2h + s) p(2h + s)/(2h + s) = d/(2h + s) Cancel the (2h + s) on the left side, we get: p = [B]d/(2h + s[/B])

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked. Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5. Let Level distance = L and hill distance = H. Add the times it took for each section of the walk: L/4 + H /3 + H/6 + L/4 = 5 The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL] [U]Multiply each side through by our LCD of 12[/U] 3L + 4H + 2H + 3L = 60 [U]Combine like terms:[/U] 6L + 6H = 60 [U]Divide each side by 3:[/U] 2L + 2H = 20 The woman walked [B]20 miles[/B]

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel if 3 pages = 5 hours, then we divide each side by 3 to get: 1 page = 5/3 hours per page So x pages takes: 5x/3 hours Our function for number of pages x is: [B]f(x) = 5x/3[/B]

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo? Let p be the total number penguins at the zoo. We're told: 30% of p = 15 Since 30% = 0.3, we have: 0.3p = 15 Solve for [I]p[/I] in the equation 0.3p = 15 [SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE] 0.3p/0.3 = 15/0.3 p = [B]50[/B]

a/m - b = c for m Add b to both sides: a/m - b + b = c + b Cancel b on both sides: a/m = c + b Multiply each side by m: am/m = m(c + b) Cancel the m's on the left side: a = m(c + b) Divide each side by (c + b) a/(c + b) = m(c + b)/(c + b) Cancel the (c + b) on the right side, and we get: m[B] = a/(c + b)[/B]

A=0.5(bh), for h Divide each side by 0.5b [B]h = A/0.5b[/B]

Multiply through: A = 2l + 2w To solve for l, subtract 2w from each side: 2l = A - 2w Divide each side by 2 l = (A - 2w)/2

Multiply through using the distributive property, so we have: A = 2l + 2w Subtract 2l from each side 2w = A - 2l Divide each side by w w = (A - 2l)/2 [MEDIA=youtube]Nm-tYD4aEY4[/MEDIA]

ab/d + c = e for d I know this is a literal equation because we are asked to solve for a variable [U]in terms of[I] another variable [/I][/U] Subtract c from each side to isolate the d term: ab/d + c - c = e - c Cancel the c's on the left side and we get: ab/d = e - c Cross multiply: ab = d(e - c) Divide each side of the equation by (e - c): ab/(e - c)= d(e - c)/(e - c) Cancel the (e - c) on the right side, and we get: d = [B]ab/(e - c)[/B]

ab/d+c=e for d Subtract c from each side: ab/d+c - c = e - c ab/d = e - c Multiply each side by d: abd/d = d(e - c) ab = d(e - c) Divide each side by (e - c): ab/(e - c) = d(e - c)/(e - c) d =[B] ab/(e - c)[/B]

Free Absolute Value Calculator - Add, subtract, multiply or divide any two numbers with absolute value signs. Positive Difference.

acw+cz=y for a Solve this literal equation: Subtract cz from each side: acw + cz - cz = y - cz Cancel the cz on the left side: acw = y - cz Divide each side by cw to isolate a: acw/cw = (y - cz)/cw Cancel cw on the left side: [B]a = (y - cz)/cw[/B]

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed was 30 mph. What was his average speed for the round trip to school and back? D = rt To school: 60 miles in 60 minutes = 10 miles in 10 minutes To home: 30 miles in 60 minutes = 10 miles in 20 minutes Total time: 10 + 20 = 30 minutes or 0.5 hours With a speed of s, we have: d = st 20 = 0.5s Divide each side by 2: s = [B]40 mph[/B]

Add 5 to p, then divide the sum by 4 Add 5 to p: p + 5 Divide the sum by 4: [B](p + 5)/4 [/B] note: B[I]ecause this is a sum, we wrap it in parentheses to divide the sum by a number[/I]

Add 7 to a, and divide the sum by b Add 7 to a: a + 7 Divide the sum by b: [B](a + 7)/b[/B]

add 8 and 10 then divide u Add 8 and 10 8 + 10 Divide by u (8 + 10)/u Simplified, it is 18/u

add c to d, multiply a by the result, then divide what you have by b Add c to d: d + c Multiply a by the result: a(d + c) then divide what you have by b: [B]a(d + c)/b[/B]

Add q to p, add a to the result, then divide r by what you have Add q to p: p + q Add a to the result: p + q + a Then divide r by what you have: [B]r/(p + q + a)[/B]

add r and q, divide the result by s, then triple what you have Add r and q: r + q Divide the result by s. The result above is r + q, so we have: (r + q)/s Triple what you have means we multiply the expression above by 3: [B]3(r + q)/s[/B]

add r to 3, triple the result, then divide s by what you have Take this algebraic expression in parts: [LIST=1] [*]Add r to 3: 3 + r [*]Triple the result means multiply the result above by 3: 3(3 + r) [*]Then divide s by what you have. [B]s/3(3 + r)[/B] [/LIST]

add u and t divide s by the result then triple what you have Take this algebraic expression in parts: [LIST] [*]Add u and t: u + t [*]Divide s by the result: s/(u + t) [*]Triple what you have means we you multiply s/(u + t) by 3 [/LIST] [B]3s/(u + t)[/B]

add w to t, add u to the result, then divide what you have by v Take this algebraic expression in parts: [LIST] [*]Add w to t: t + w [*]Add u to the result: t + w + u [*]Divide what you have by v: [/LIST] ([B]t + w + u)/v[/B]

Let f be the age of the father and d be the age of the daughter and s be the age of the son. We have: [LIST=1] [*]f = 3s [*]d = s - 3 [*]d - 3 + f - 3 + s - 3 = 63 [/LIST] Simplify (3) d + f + s - 9 = 63 d + f + s = 72 Now, substitute (1) and (2) into the modified (3) (s - 3) + 3s + s = 72 Combine like terms: 5s - 3 = 72 Add 3 to each side 5s = 75 Divide each side by 5 s = 15 We want f, so we substitute s = 15 into (1) f = 3(15) [B]f = 45[/B]

Alex sells cars at Keith Palmer ford. He earns 400 dollars a week plus 150 dollars per car he sells. If he earned 1450 dollars last week, how many cars did he sell? Subtract the base salary of $400 $1,450 - 400 =$1,050 Divide this by 150 per car $1,050/$150 = [B]7 cars[/B]

Free Algebraic Expressions Calculator - This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times) Also known as Mathematical phrases

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age? Let a be Alvin's age and e be Elga's age. We have the following equations: [LIST=1] [*]a = e - 12 [*]a + e = 60 [/LIST] Plugging in (1) to (2), we get: (e - 12) + e = 60 Grouping like terms: 2e - 12 = 60 Add 12 to each side: 2e = 72 Divide each side by 2 [B]e = 36[/B]

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time? Total weight = average weight per person * Number of people Total weight = 150p We know from the problem that: 150p < 2700 We want to solve this inequality for p. Divide each side of the inequality by 150: 150p/150 < 2700/150 Cancel the 150's on the left side and we get: p < [B]18[/B]

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours over 35. One weeks paycheck (before deductions) was for $308.00. How many hours did the employee work? Let's first check to see if the employee worked overtime: Regular Hours: 35 * 7 = 245 Since the employee made $308, they worked overtime. Let's determine how much overtime money was made: 308 - 245 = 63 Now, to calculate the overtime hours, we divide overtime pay by overtime rate 63/10.50 = 6 Now figure out the total hours worked in the week: Total Hours = Regular Pay Hours + Overtime Hours Total Hours = 35 + 6 [B]Total Hours = 41[/B]

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone? Person A: x/2 job per hour Person B: 1/x job per hour Set up our equation: 1/x + 1/(2x) = 1/10 Multiply the first fraction by 2/2 to get common denominators; 2/(2x) + 1/(2x) = 1/10 Combine like terms 3/2x = 1/10 Cross multiply: 30 = 2x Divide each side by 2: [B]x = 15[/B]

Ana has 24 carrots, 12 cucumbers, and 36 radishes. She wants to make identical vegetable baskets using all of the vegetables. What is the greatest number of baskets she can make The key to solving this problem is asking what is the common factor between the 3 numbers. We want the greatest common factor or GCF [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=24&num3=36&pl=GCF']GCF(12, 24, 36) [/URL]= [B]12[/B] We divide up our 12 baskets into carrots, cucumbers, and radishes. Each basket of the 12 baskets has the following: [LIST=1] [*]12 cucumbers / GCF of 12 = [B]1 cucumber per basket[/B] [*]24 carrots / GCF of 12 = [B]2 carrots per basket[/B] [*]36 radishes / GCF of 12 = [B]3 radishes per basket[/B] [/LIST] [B][MEDIA=youtube]D1KTOP0h2P4[/MEDIA][/B]

Anita read 150 pages in 5 hours. What is her reading rate in pages per minute? 150 pages / 5 hours Divide top and bottom by 5: 150/5 = 30 5/5 = 1 So we have 30 pages per hour And 1 hour is 60 minutes, so we have: (30 pages / 1 hour) * (1 hour / 60 minutes) 30 pages / 60 minutes [B]0.5 pages per minute[/B]

anne is building bookcases that are 3.4 feet long. How many complete shelves can be cut from a 12-foot board? We divide 12 feet of board by 3.4 per bookcase and we get: 12/3.4 = 3.52 So complete boards = [B]3[/B]

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job? Area of platform which is a rectangle: A = lw A = 10 * 7 A = 70 Area of boards which are rectangles: A = lw A = 2 * 6 A = 12 We divide our platform area by our board area to get the number of boards needed: Boards needed = Platform Area / Board Area Boards needed = 70/12 Boards needed = 5.83333 We round up if we want full boards to be [B]6[/B]

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have? Let the April sweets be a. Let the May sweets be m. Let the June sweets be j. We're given the following equations: [LIST=1] [*]m = 3j/4 [*]a = 2m/3 [*]a + j + m = 90 [/LIST] Cross multiply #2; 3a = 2m Dividing each side by 2, we get; m = 3a/2 Since m = 3j/4 from equation #1, we have: 3j/4 = 3a/2 Cross multiply: 6j = 12a Divide each side by 12: a = j/2 So we have: [LIST=1] [*]m = 3j/4 [*]a = j/2 [*]a + j + m = 90 [/LIST] Now substitute equation 1 and 2 into equation 3: j/2 + j + 3j/4 = 90 Multiply each side by 4 to eliminate fractions: 2j + 4j + 3j = 360 To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get: j = [B]40[/B]

Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit was $2.40. How many bagels did he buy? Let x be the number of bagels Arnie sold. We have the following equation: 0.30(x - 4) - 0.20(4) = 2.40 Distribute and simplify: 0.30x - 1.20 - 0.8 = 2.40 Combine like terms: 0.30x - 2 = 2.40 Add 2 to each side: 0.30x = 4.40 Divide each side by 0.3 [B]x = 14.67 ~ 15[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100? Set up the inequality where s is the amount of sales you make: 50 + 2s >= 100 We use >= because the phrase [I]at least[/I] 100 means 100 or more Subtract 50 from each side: 2s >= 50 Divide each side by 2 [B]s >= 25[/B]

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same? Set up the cost functions where x is the number of aerobics classes: [LIST] [*]Members: C(x) = 10 + 3x [*]Non-members: C(x) = 5x [/LIST] Set them equal to each other 10 + 3x = 5x Subtract 3x from both sides: 2x = 10 Divide each side by 2 [B]x = 5 classes[/B]

At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members be equal to nonmembers? Set up two cost equations C(x): [LIST=1] [*]Members: C(x) = 8 + 3x [*]Nonmembers: C(x) = 5x [/LIST] Set the two cost equations equal to each other: 8 + 3x = 5x Subtract 3x from each side 2x = 8 Divide each side by 2 [B]x = 4[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2. [LIST] [*]How many men at the party? [*]How many ladies at the party? [*]How many kids at the party? [/LIST] Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party [U]Calculate ratios:[/U] [LIST] [*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B] [*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B] [*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B] [/LIST] [U]Check our work:[/U] Men + Ladies + Kids = 32 + 24 + 16 Men + Ladies + Kids = 72 <-- This checks out!

At the end of the day, a bakery had 1/2 of a pie left over. The 4 employees each took home the same amount of leftover pie. How much pie did each employee take home? We have 1/2 of the pie eaten, if 1/2 was left over. So 1/2 of a pie divided by 4 employees = [B]1/8 of a pie per person[/B]. To check our work, we have 4 * 1/8 = 4/8 = 1/2 of pie eaten.

At what simple interest rate will 4500$ amount to 8000$ in 5 years? Simple Interest is written as 1 + it. With t = 5, we have: 4500(1 + 5i) = 8000 Divide each side by 4500 1 + 5i = 1.77777778 Subtract 1 from each side: 5i = 0.77777778 Divide each side by 5 i = 0.15555 As a percentage we multiply by 100 to get [B]15.5%[/B]

[B]A[/B]t Zabowood�s Gadget Store, some items are paid on instalment basis through credit cards. Clariza was able to sell 10 cellphones costing Php 18,000.00 each. Each transaction is payable in 6 months equally divided into 6 equal instalments without interest. Clariza gets 2% commission on the first month for each of the 10 cellphones. Commission decreases by 0.30% every month thereafter and computed on the outstanding balance for the month. How much commission does Clariza receive on the third month? Calculate Total Sales Amount: Calculate Total Sales Amount = 10 cellphones * 18000 per cellphone Calculate Total Sales Amount = 180000 Calculate monthly sales amount installment: monthly sales amount installment = Total Sales Amount / 6 monthly sales amount installment = 180000/6 monthly sales amount installment = 30000 per month Calculate Third Month Commission: Third month commission = First Month Commission - 0.30% - 0.30% Third month Commission = 2% - 0.30% - 0.30% = 1.4% Calculate 3rd month commission amount: 3rd month Commission amount = 1.4% * 30000 3rd month Commission amount = [B]420[/B]

Ava is 4 times as old as Peter. What equation can be used to find Peter�s age? [U]Assumptions[/U] Let a be Ava's age Let p be Peter's age We're given: a = 4p To find Peter's age, we divide each side of the equation by 4 to get: a/4 = 4p/4 p = [B]a/4[/B]

We are solving for x: Subtract b from each side: ax = cx - d - b Subtract cx from each side: ax - cx = -d - b Factor out x from the left side: x(a - c) = -d - b Divide each side by (a - c) x = (-d - b)/(a - c)

ax - mn = mn + bx for x Add mn to each side: ax - mn + mn = mn + bx + mn Cancel the mn terms on the left side and we get: ax = bx + 2mn Subtract bx from each side: ax - bx = bx - bx + 2mn Cancel the bx terms on the right side: ax - bx = 2mn Factor out x on the left side: x (a - b) = 2mn Divide each side of the equation by (a - b): x (a - b)/(a - b) = 2mn/(a - b) Cancel the (a - b) on the left side and we get: x = [B]2mn/(a - b)[/B]

B is the midpoint of AC and BC=5 Since the midpoint divides a segment into two equal segments, we know that: AB = BC So AB =[B] 5[/B] And AC = 5 + 5 = [B]10[/B]

B+c =10/a for a Cross multiply: a(B + c) = 10 Divide each side by a [B]a = 10/(B + c)[/B]

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Let w be the number of weeks that go by for saving/spending. Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U] B(w) = Initial Amount - spend per week * w weeks B(w) = 450 - 3w Set up Betty's balance equation, B(w). Saving means we [U]add[/U] B(w) = Initial Amount + savings per week * w weeks B(w) = 120 + 8w The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w: 450 - 3w = 120 + 8w Add 3w to each side to isolate w: 450 - 3w + 3w = 120 + 8w + 3w Cancelling the 3w on the left side, we get: 450 = 120 + 11w Rewrite to have constant on the right side: 11w + 120 = 450 Subtract 120 from each side: 11w + 120 - 120 = 450 - 120 Cancelling the 120's on the left side, we get: 11w = 330 To solve for w, we divide each side by 11 11w/11 = 330/11 Cancelling the 11's on the left side, we get: w = [B]30 [MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

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Free Basic Math Operations Calculator - Given 2 numbers, this performs the following arithmetic operations:
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Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D) a) The equation is: [B]0.1d + 0.25q = 4.5[/B] b) Isolate the equation for d. We subtract 0.25q from each side of the equation: 0.1d + 0.25q - 0.25q = 4.5 - 0.25q Cancel the 0.25q on the left side, and we get: 0.1d = 4.5 - 0.25q Divide each side of the equation by 0.1 to isolate d: 0.1d/0.1 = (4.5 - 0.25q)/0.1 d = [B]45 - 2.5q[/B]

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the return trip she went 30 km/h. How long did the trip there take if the return trip took six hours? We use the distance formula: D = rt where D = distance, r = rate, and t = time. Start with the return trip: D = 45(6) D = 270 The initial trip is: 270= 30t Divide each side by 30 [B]t = 9 hours[/B]

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to have written a total of 16 pages? [U]Let x = the number of hours Blake needs to write[/U] 4 pages per hour * x hours = 16 [U]Divide each side by 4[/U] [B]x = 4 hours[/B]

Bob can complete 35 math problems in 5 minutes how many can he complete in 1 minute 35 math problems / 5 minutes Divide the top and bottom of the fraction by 5: 35 math problems / 5 minutes =[B] 7 math problems per minute[/B]

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will both of them get? If Bob shares the fudge with Sue, we assume they split equal parts. This means: We take 4/5 total and divide into 2 for 2 people: 4/5/2 This is the same as 4/5 * 1/2 4/10 This fraction is not simplified. Factor of 4 = {1, [U]2[/U], 4} Factors of 10 = {1, [U]2[/U], 5, 10} In both of these lists, we see the greatest common factor is 2. So we divide top and bottom of 4/10 by 2: 4/2 / 10 / 2 [B]2/5 Bob gets 2/5 of a pound of fudge and Sue gets [B]2/5 of a pound of fudge[/B][/B]

Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his paycheck. How many weeks will it take until he saves 3000? Remaining Savings = 3,000 - 1,200 = 1,800 40 per week * x weeks = 1,800 40x = 1800 Divide each side of the equation by 40 [B]x = 45 weeks[/B]

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month. Let x equal to the number room movie rentals per month. Our inequality is: 120 + 2.99x < 150 To solve for the number of movies, Add 120 to each side 2.99x < 30 Divide each side by 2.99 x < 10.03, which means 10 since you cannot buy a fraction of a movie

by + 2/3 = c for y Subtract 2/3 from each side of the literal equation: by + 2/3 - 2/3 = c - 2/3 Cancel the 2/3 on the left side to get: by = c - 2/3 Divide each side by b to isolate y: by/b = (c - 2/3)/b Cancel the b's on the left side to get: y = [B](c - 2/3)/b[/B]

by + 2/3 = c, for y Subtract 2/3 from each side: by = c - 2/3 Divide each side by b y = [B](c - 2/3)/b[/B]

b^2 - 6 = 5an for a Divide each side of the equation by 5n to isolate a: (b^2 - 6)/5n = 5an/5n Cancel the 5n on the right side and we get: a = [B](b^2 - 6)/5n[/B]

C varies directly as the cube of a and inversely as the 4th power of B The cube of a means we raise a to the 3rd power: a^3 The 4th power of B means we raise b to the 4th power: b^4 Varies directly means there exists a constant k such that: C = ka^3 Also, varies inversely means we divide by the 4th power of B C = [B]ka^3/b^4[/B] Varies [I]directly [/I]as means we multiply by the constant k. Varies [I]inversely [/I]means we divide k by the term which has inverse variation. [MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

c/a=db/r for a Cross multiply the proportion: cr = adb Divide each side of the equation by db to isolate a: cr/db = adb/db Cancel the db terms on the left side and we get: a = [B]cr/db[/B]

c=59f-288 for f Add 288 to each side: c + 288 = 59f - 288 + 288 Cancel the 288 on the right side, we get: 59f = c + 288 Divide each side by 59 to isolate f: 59f/59 = (c + 288)/59 Cancel the 59 on the left side, we get: f = [B](c + 288)/59[/B]

calculate cos(x) given tan(x)=8/15 tan(x) = sin(x)/cos(x) sin(x)/cos(x) = 8/15 Cross multiply: 15sin(x) = 8cos(x) Divide each side by 8 [B]cos(x) = 15sin(x)/8[/B]

Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases. [U]Set up our equations:[/U] (1) 4f + 2h + p = 14660 (2) f + h + p = 9480 (3) f = 2h + 140 [U]First, substitute (3) into (2)[/U] (2h + 140) + h + p = 9480 3h + p + 140 = 9480 3h + p = 9340 [U]Subtract 3h to isolate p to form equation (4)[/U] (4) p = 9340 - 3h [U]Take (3) and (4), and substitute into (1)[/U] 4(2h + 140) + 2h + (9340 - h) = 14660 [U]Multiply through[/U] 8h + 560 + 2h + 9340 - 3h = 14660 [U]Combine h terms and constants[/U] (8 + 2 - 3)h + (560 + 9340) = 14660 7h + 9900 = 14660 [U]Subtract 9900 from both sides:[/U] 7h = 4760 [U]Divide each side by 7[/U] [B]h = 680[/B] [U]Substitute h = 680 into equation (3)[/U] f = 2(680) + 140 f = 1360 + 140 [B]f = 1,500[/B] [U] Substitute h = 680 and f = 1500 into equation (2)[/U] 1500 + 680 + p = 9480 p + 2180 = 9480 [U]Subtract 2180 from each side:[/U] [B]p = 7,300[/B]

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age Declare variables for each age: [LIST] [*]Let Casey's age be c [*]Let her daughter's age be d [*]Let n be the number of years from now where Casey will be double her daughter's age [/LIST] We're told that: 26 + n = 2(4 + n) 26 + n = 8 + 2n Solve for [I]n[/I] in the equation 26 + n = 8 + 2n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 2n. To do that, we subtract 2n from both sides n + 26 - 2n = 2n + 8 - 2n [SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE] -n + 26 = 8 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 26 and 8. To do that, we subtract 26 from both sides -n + 26 - 26 = 8 - 26 [SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE] -n = -18 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -18/-1 n = [B]18[/B] Check our work for n = 18: 26 + 18 ? 8 + 2(18) 44 ? 8 + 36 44 = 44

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Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope? Equal length means we divide the length of the rope by the number of equal cuts [B]8/3 or 2 & 2/3 meters[/B]

Chris walks 12 blocks north and then 16 blocks East. How far is his home from the park We've got a right triangle. If we divide 12 and 16 by 4, we get: 12/4 = 3 16/4 = 4 Since the hypotenuse is the distance from the home to the park, we have a classic 3-4-5 right triangle. So our hypotenuse is 5*4 = [B]20[/B]

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age [LIST=1] [*]a = c + 5 [*]j = a + 6 [*]a + c + j = 31 [*]Rearrange (1) in terms of c: c = a - 5 [/LIST] [U]Plug in (4) and (2) into (3)[/U] a + (a - 5) + (a + 6) = 31 [U]Combine like terms:[/U] 3a + 1 = 31 [U]Subtract 1 from each side[/U] 3a = 30 [U]Divide each side by 3[/U] [B]a = 10[/B] [U]Plug in 1 = 10 into Equation (4)[/U] c = 10 - 5 [B]c = 5[/B] Now plug 1 = 10 into equation (2) j = 10 + 6 [B]j = 16[/B]

Cindy is c years old. Cindy is 5 years younger than half Jennifer's age ( j ) Build an algebraic expression: [B]c = j/2 - 5[/B] <-- Half means we divide by 2 and [I]younger[/I] means we subtract

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens? (All candies and pens should be used.) We want the greatest common factor of 180 and 140. When we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=140&num2=180&num3=&pl=GCF+and+LCM']run GCF(180,140) in our calculator[/URL], we get 20. We divide our total candies and total pens by our GCF. So each bag has the following: Candies: 180/20 = [B]9 candies[/B] Pens: 140/20 = [B]7 pens[/B]

cody takes about 24,040 breaths a day. how many breaths is that in an hour? There are 24 hours in a day, so we divide 24,040 / 24 to get breaths per hour: 24,040 / 24 = [B]1001.67 [/B]

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number? Let the number be n. Divide by 8: n/8 Then add 1: n/8 + 1 The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2: n/8 + 1 = 2 To solve for n, we subtract 1 from each side to isolate the n term: n/8 + 1 - 1 = 2 - 1 Cancel the 1's on the left side, we get: n/8 = 1 Cross multiply: n = 8*1 n = [B]8[/B]

Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would you need to travel to get each charge to be the same? Let x be the number of miles traveled Company A charge: C = 25 + 0.10x Company B charge: C = 20 + 0.15x Set up an equation find out when the charges are the same. 25 + 0.10x = 20 + 0.15x Combine terms and simplify 0.05x = 5 Divide each side of the equation by 0.05 to isolate x x = [B]100[/B]

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Connie�s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group? We take 24 children divided by 4 equal groups = 24/4 24/4 = [B]6 children per group[/B]

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate. The variable "h" is the easiest to solve for. Because you only have one step. Let's review: Divide each side of the equation by 12(a + b) h = 12(a + b)/A Solving for "a", we two steps. Divide each side by 12h: A/12h = a + b Subtract b from each side a = A/12h - b Solving for "b" takes two steps as well. Divide each side by 12h: A/12h = a + b Subtract a from each side b = A/12h - a

cot(?)=12 and ? is in Quadrant I, what is sin(?)? cot(?) = cos(?)/sin(?) 12 = cos(?)/sin(?) Cross multiply: 12sin(?) = cos(?) Divide each side by 12: sin(?) = [B]12cos(?)[/B]

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country. Set up our two given equations: [LIST=1] [*]A = 7B [*]A + B = 40,000,000 [/LIST] Substitute (1) into (2) (7B) + B = 40,000,000 Combine like terms 8B = 40,000,000 Divide each side by 8 [B]B = 5,000,000[/B] Substitute this into (1) A = 7(5,000,000) [B]A = 35,000,000[/B]

d - f^3 = 4a for a Solve this literal equation for a: Divide each side of the equation by 4: (d - f^3)/4 = 4a/4 Cancel the 4's on the right side, and rewrite with our variable to solve for on the left side: a = [B](d - f^3)/4[/B]

Dan makes 11 an hour working at the local grocery store. Over the past year he has saved 137.50 toward a new pair of retro sneakers. If sneakers cost 240, how many hours will he need to be able to buy the sneakers? Figure out his remaining savings target: 240 - 137.50 = 102.50 Let x equal the number of remaining hours Dan needs to work 11x = 102.50 Divide each side by 11 x = 9.318 We round up for a half-hour to 9.5, or a full hour to 10.

Dan needs 309 programs for the school play on Thursday. How many boxes of programs will he need, given that each box contains 41 programs? Each box contains 41 programs, so we divide 309 programs by 41 programs per box to get our boxes: 309/41 using our [URL='https://www.mathcelebrity.com/longdiv.php?num1=309&num2=41&pl=Long%20Division%20%28Decimals%29']division calculator[/URL] is 7.5365. Since we don't have fractional boxes, we round up to the next highest integer. [B]8 boxes[/B]

Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. How much of the cake would each get? If Danny's mom ate 1/6 of the cake, then we have: 1 - 1/6 of the cake left. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F6&pl=Subtract']use our fraction subtraction calculator[/URL] for 1 - 1/6 to get: 5/6 If Danny and his sister split the remainder, then we divide 5/6 by 2. It's also the same as multiplying 5/6 by 1/2: We [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F6&frac2=1%2F2&pl=Multiply']use our fraction multiplication calculator[/URL] to get: [B]5/12 for Danny and his sister[/B]

Debra buys candy that costs 4 per pound. She will spend less than 20 on candy. What are the possible numbers of pounds she will buy? Set up an inequality using less than < and p for pounds: 4p < 20 Divide each side by 4: 4p/4 < 20/4 [B]p < 5[/B]

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left over, how much did each person eat? This means 4 full pizzas - 1/4 of a pizza = 3 & 3/4 pizzas eaten Del and his 5 friends means 6 people total. Since they ate equal amounts, we divide pizzas eaten by total people: 3 & 3/4 / 6 Convert 3 & 3/4 to a mixed fraction: (4*3 + 3)/4 = 15/4 15/4/6 Divide by a fraction is the same as multiply by a reciprocal: 15/4 * 1/6 = [B]15/24 pizzas per person[/B]

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day? Setup distance ran for the 7 days: [LIST=1] [*]n [*]n + 1 [*]n + 2 [*]n + 3 [*]n + 4 [*]n + 5 [*]n + 6 [/LIST] Add them all up: 7n + 21 = 70 Solve for [I]n[/I] in the equation 7n + 21 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 21 and 70. To do that, we subtract 21 from both sides 7n + 21 - 21 = 70 - 21 [SIZE=5][B]Step 2: Cancel 21 on the left side:[/B][/SIZE] 7n = 49 [SIZE=5][B]Step 3: Divide each side of the equation by 7[/B][/SIZE] 7n/7 = 49/7 n =[B] 7 [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B21%3D70&pl=Solve']Source[/URL][/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money? We set up a balance equation B(m) where m is the number of months. [U]Set up Deon's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 650 - 40m [U]Set up Mai's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 850 - 65m When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m: 650 - 40m = 850 - 65m Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -40m and -65m. To do that, we add 65m to both sides -40m + 650 + 65m = -65m + 850 + 65m [SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE] 25m + 650 = 850 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 650 and 850. To do that, we subtract 650 from both sides 25m + 650 - 650 = 850 - 650 [SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE] 25m = 200 [SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE] 25m/25 = 200/25 m = [B]8[/B]

Determine whether the statement is true or false. You can always divide by e^x [B]True. As x --> infinity, 1/e^x approaches 0 but never touches it.[/B]

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12. Our givens are: [LIST] [*]I = 450 [*]P = 3000 [*]t = 3 [*]We want r [/LIST] 450 = 3000(r)(3) 450 = 9000r Divide each side by 9000 [B]r = 0.05[/B]

Difference of a and b, divided by 2. The difference of a and b is written as: a - b We divide this by 2: [B](a - b)/2[/B]

Divide 17 by g. Then, subtract 9. Divide 17 by g 17/g Subtract 9 [B]17/g - 9[/B]

Divide 73 into two parts whose product is 40 Our first part is x Our second part is 73 - x The product of the two parts is: x(73 - x) = 40 Multiplying through, we get: -x^2 + 73x = 402 Subtract 40 from each side, we get: -x^2 + 73x - 402 = 0 This is a quadratic equation. To solve this, we type it in our search engine, choose "solve Quadratic", and we get: [LIST=1] [*]x = [B]6[/B] [*]x = [B]67[/B] [/LIST]

divide 8 by 9, then subtract t Divide 8 by 9 8/9 Then subtract t [B]8/9 - t[/B]

divide 8 by t, raise the result to the 7th power. We take this algebraic expression in two parts: 1. Divide 8 by t 8/t 2. Raise the result to the 7th power. (This means we use an exponent of 7) [B](8/t)^7[/B]

divide a by 8, triple the result, then add 7 [LIST] [*]Divide a by 8: a/8 [*]Triple the result means multiply by 3: 3a/8 [*]Then add 7 [/LIST] [B]3a/8 + 7[/B]

Divide a by b, double the result, then multiply c by what you have Take this algebraic expression in parts: [LIST] [*]Divide a by b: a/b [*]Double the result means multiply by 2: 2a/b [*]Then multiply c by what you have: [/LIST] [B]2ac/b[/B]

divide a by c, triple the result, then subtract what you have from b Let's take this algebraic expression in parts: [LIST=1] [*]Divide a by c: a/c [*]Triple the result. This means we multiply a/c by 3: 3a/c [*]Then subtract what you have (the result) from b: b - 3a/c [/LIST] [B]b - 3a/c[/B]

Divide a number by 10. Then, add 10. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Divide the number by 10 mean we have a quotient, of x over 10 x / 10 Then, add 10: [B](x / 10) + 10[/B]

divide b by a, subtract the result from c, then add what you have to d Take this algebraic expression in 3 parts: [U]1) Divide b by a:[/U] b/a [U]2) Subtract the result from c:[/U] c - b/a [U]3) Then add what you have to d:[/U] [B]c - b/a + d[/B]

divide d by a, add the result to b, then add c [LIST] [*]Divide d by a: d/a [*]add the result to b: b + d/a [*]Then add c [/LIST] [B]b + d/a + c[/B]

Divide m by 3 and then add 10 Divide m by 3: m/3 Then add 10: [B]m/3 + 10[/B]

Divide the difference of 4 and r by 10 The difference of 4 and r, mean we subtract r from 4: 4 - r Now we divide this expression by 10: [B](4 - r)/10 [/B]

divide the difference of q and s by the sum of p and r Take this algebraic expression in pieces: [LIST] [*]The difference of q and s: q - s [*]The sum of p and r: p + r [*]The word [I]divide[/I] means we divide q - s by p + r [/LIST] [B](q - s)/(p + r)[/B]

Divide the sum of a and b by the square of c The sum of a and b: a + b The square of c means we raise c to the power of 2: c^2 Divide means we have a quotient, with a + b on top, and c^2 on the bottom: [B](a + b)/c^2[/B]

divide the sum of the square of a and b by thrice c Sum of the squares of a and b is found as follows: [LIST] [*]a squared means we raise a to the power of 2: a^2 [*]b squared means we raise b to the power of 2: b^2 [*]Sum of the squares means we add both terms: a^2 + b^2 [*]Thrice c means we multiply c by 3: 3c [/LIST] Divide means we have a quotient: [B](a^2 + b^2)/3c[/B]

Divide the sum of the squares of a and b by the square of c square of a: a^2 square of b: b^2 Sum of the squares of a and b: a^2 + b^2 square of c: c^2 Divide the Sum of the squares of a and b by the square of c: [B](a^2 + b^2)/c^2[/B]

Divide the sum x and y by the difference of subtracting a from b The sum x and y is written as: x + y The difference of subtracting a from b is written as: b - a We divide and get the algebraic expression: [B](x + y)/(b - a)[/B]

divide u by s multiply the result by v Divide u by s: u/s Multiply the result by v: [B]uv/s[/B]

divide u by s, then subtract the result from t Divide u by s: u/s Subtract the result from t: [B]t - u/s[/B]

divide u by w add the result to v Divide u by w: u/w Add the result to v: [B]v + u/w[/B]

Divide v by the sum of 4 and w The sum of 4 and w means we add w to 4: 4 + w Next, we divide v by this sum to get our final algebraic expression: [B]v/(4 + w)[/B]

Divide x by 2.2, and then add 2.2 to the quotient. Divide x by 2.2 (This is a quotient): x/2.2 Then add 2.2 to the quotient [B]x/2.2 + 2.2[/B]

Divide x cubed by the quantity x minus 7 x cubed means we raise x to the power of 3: x^3 We divide this by x - 7: [B]x^3/(x - 7)[/B]

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double 6 , divide the result by y ,then raise what you have to the 10th power Take this in pieces: Double 6 means multiply 6 by 2 --> 6(2) = 12 Divide the result by y: 12/y Then raise what you have to the 10th power: [B](12/y)^10[/B]

double v, add u, then divide t by what you have Double v means we multiply the variable v by 2: 2v Add u: 2v + u We build a fraction, with t as the numerator, and 2v + u as the denominator [B]t/(2v + u)[/B]

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company Declare variables: [LIST] [*]Let b be the number of business cards. [/LIST] [U]Set up the cost function C(b) for Dunder Mifflin:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.1b + 15 [U]Set up the cost function C(b) for Werham Hogg:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.15b + 10 The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b: 0.1b + 15 = 0.15b + 10 Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides 0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b [SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE] -0.05b + 15 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 15 and 10. To do that, we subtract 15 from both sides -0.05b + 15 - 15 = 10 - 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] -0.05b = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE] -0.05b/-0.05 = -5/-0.05 b = [B]100[/B]

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 19, 9, 14, 10, 16, 17. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth. The mean is the average, so we add up the 6 movie scores, and divide by 6. [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = Sum of 6 Movie Scores / 6 [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 84 / 6 [URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 14.16666667 The problem asks us to round to the nearest tenth, which is the first decimal place. Since the 2nd decimal place, 6 is more than 5, we round the first decimal place up one and remove the rest. [B]14.2[/B]

the quantity y plus two y + 2 the quantity y plus two divided by four (y +2)/4 Eight times the quantity y plus two divided by four 8(y +2)/4 8/4 = 2, so we have: [B]2(y +2) or 2y + 4 [MEDIA=youtube]xzwaXi6N1uI[/MEDIA][/B]

Emily is three years older than twice her sister Mary�s age. The sum of their ages is less than 30. What is the greatest age Mary could be? Let e = Emily's age and m = Mary's age. We have the equation e = 2m + 3 and the inequality e + m < 30 Substitute the equation for e into the inequality: 2m + 3 + m < 30 Add the m terms 3m + 3 < 30 Subtract 3 from each side of the inequality 3m < 27 Divide each side of the inequality by 3 to isolate m m < 9 Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.

Equation 2y+5x=40. Interprt the intercepts Y intercept is when X = 0 2y + 5(0) = 40 2y = 40 Divide each side by 2 [B]y = 20 [/B] X intercept is when Y = 0 2(0) + 5x = 40 5x = 40 Divide each side by 5 [B]x = 8[/B]

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have? Number of stamps: [LIST] [*]Number of 37 cent stamps = s [*]Number of 3-cent stamps = 3s [*]Number of 5-cent stamps = 0.5s [/LIST] Value of stamps and coins: [LIST] [*]37 cent stamps = 0.37s [*]3-cent stamps = 3 * 0.03 = 0.09s [*]5-cent stamps = 0.5 * 0.05s = 0.025s [*]Quarter, 2 dime, 7 pennies = 0.52 [/LIST] Add them up: 0.37s + 0.09s + 0.025s + 0.52 = 8.28 Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (0.37 + 0.09 + 0.025)s = 0.485s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.485s + 0.52 = + 8.28 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides 0.485s + 0.52 - 0.52 = 8.28 - 0.52 [SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE] 0.485s = 7.76 [SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE] 0.485s/0.485 = 7.76/0.485 s = [B]16[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept Get this in slope-intercept form by adding 5y to each side: 4x - 5y + 5y = 5y + 20 Cancel the 5y's on the left side and we get: 5y + 20 = 4x Subtract 20 from each side 5y + 20 - 20 = 4x - 20 Cancel the 20's on the left side and we get: 5y = 4x - 20 Divide each side by 5: 5y/5 = 4x/5 - 4 y = 4x/5 - 4 So we have a slope of 4/5 to find our y-intercept, we set x = 0: y = 4(0)/5 - 4 y = 0 - 4 y = -4 If we want a line perpendicular to the line above, our slope will be the negative reciprocal: The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator: m = 5/4 Next, we multiply this by -1: -5/4 So our slope-intercept of the perpendicular line with the same y-intercept is: [B]y = -5x/4 - 4[/B]

ey/n + k = t for y Let's take this literal equation in pieces: Subtract k from each side: ey/n + k - k = t - k Cancel the k's on the left side, we have: ey/n = t - k Now multiply each side by n: ney/n = n(t - k) Cancel the n's on the left side, we have: ey = n(t - k) Divide each side by e: ey/e = n(t - k)/e Cancel the e's on the left side, we have: [B]y = n(t - k)/e[/B]

F varies directly as g and inversely as r^2 [U]Givens and assumptions[/U] [LIST] [*]We take a constant of variation called k. [*][I]Varies directly means we multiply our variable term by k[/I] [*][I]Varies inversely means we divide k by our variable term[/I] [/LIST] The phrase varies directly or varies inversely means we have a constant k such that: [B]F = kg/r^2[/B]

f varies jointly with u and h and inversely with the square of y. Variation means we have a constant k. Varies jointly with u and h means we multiply k by hu Varies inversely with the square of y means we divide by y^2 [B]f = khu/y^2[/B]

f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b Set up both equations with values When x = 3, f(3) = 17, so we have a(b)^3 = 17 When x = 7, f(7) = 3156, so we have a(b)^7 = 3156 Isolate a in each equation a = 17/(b)^3 a = 3156/(b)^7 Now set them equal to each other 17/(b)^3 = 3156/(b)^7 Cross Multiply 17b^7 = 3156b^3 Divide each side by b^3 17b^4 = 3156 Divide each side by 17 b^4 = 185.6471 [B]b = 3.6912[/B]

F/B=(M-N*L)/D for L Cross multiply: DF/B = M - N*L Subtract M from each side: DF/B - M = -N*L Divide each side by -N [B]L = -DF/BN[/B]

Free Factorials Calculator - Calculates the following factorial items:
* A factorial of one number such as n!
* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!
* Double Factorials such as n!!
* Stirlings Approximation for n!

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day. We set up the function P(d) where d is the number of days sine she started losing plants: P(d) = Initial plants * (1 - Loss percent / 100)^d Plugging in our numbers, we get: 20 = 150 * (1 - 4/100)^d 20 = 150 * (1 - 0.04)^d Read left to right so it's easier to read: 150 * 0.96^d = 20 Divide each side by 150, and we get: 0.96^d = 0.13333333333 To solve this logarithmic equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=0.96%5Ed%3D0.13333333333&pl=Calculate']type it in our search engine[/URL] and we get: d = 49.35 The problem tells us to round up, so we round up to [B]50 days[/B]

Find the greatest number which divides 845 and 1250 This is the greatest common factor. We [URL='https://www.mathcelebrity.com/gcflcm.php?num1=845&num2=1250&num3=&pl=GCF+and+LCM']type GCF(845,1250) into our search engine [/URL]and we get: [B]5[/B]

Check out this pattern: 2^1= 2 2^2= 4 2^3 = 8 2^4= 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 The last digit repeats itself in blocks of 4 2, 4, 8, 6 We want to know what is the largest number in 1, 2, 3, 4 that divides 2020 without a remainder. LEt's start with 4 and work backwards. 2020/4 = 505 Ever power of 2^4(n) ends in 6, so our answer is [B]6 [MEDIA=youtube]6uX5gwb1jdY[/MEDIA][/B]

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of 7. From our [URL='http://www.mathcelebrity.com/divisibility.php?num=120&pl=Divisibility']divisibility calculator[/URL], we see a number is divisible by 9 if the sum of its digits is divisible by 9. Starting from 1 to 99, we find all numbers with a digit sum of 9. This would be digits with 0 and 9, 1 and 8, 2 and 7, 3 and 6, and 4 and 5. 9 18 27 36 45 54 63 72 81 90 Now remove even numbers since the problem asks for odd numbers 9 27 45 63 81 Now, divide each number by 10, and find the remainder 9/10 = 0 [URL='http://www.mathcelebrity.com/modulus.php?num=27mod10&pl=Calculate+Modulus']27/10[/URL] = 2 R 7 We stop here. [B]27[/B] is an odd number, less than 100, with a remainder of 7 when divided by 10.

Find the velocity of a cheetah that runs 100m in 4 seconds 100m / 4 seconds Divide top and bottom by 4 [B]25m/second[/B]

Finding a 20% tip no calculator We have 2 methods to calculate a 20% tip. [LIST=1] [*]Divide by 5 [*]Shift one decimal place left and take the value. Multiply by 2 [/LIST] Example: 180 tip, find a 20% tip: Method 1: 180/5 = 36 Method 2: Move decimal place left = 18 Multiply this value by 2: 18 * 2 = 36 [MEDIA=youtube]UW4GYWfMhsE[/MEDIA]

fixed cost 500 marginal cost 8 item sells for 30. Set up Cost Function C(x) where x is the number of items sold: C(x) = Marginal Cost * x + Fixed Cost C(x) = 8x + 500 Set up Revenue Function R(x) where x is the number of items sold: R(x) = Revenue per item * items sold R(x) = 30x Set up break even function (Cost Equals Revenue) C(x) = R(x) 8x + 500 = 30x Subtract 8x from each side: 22x = 500 Divide each side by 22: x = 22.727272 ~ 23 units for breakeven

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. How far from each side of the pages should he put the picture? Enter your answer as a mixed number. First, determine your margins, which is the difference between the width and photo width, divided by 2. 10 - 9 & 1/2 = 1/2 1/2 / 2 = [B]1/4[/B]

Fred earns $420 a month. If his monthly car payment is one quarter of his pay, how much is his car payment? 1/4 means divided by 4, so we have: Monthly Payment = Earnings/4 Monthly Payment =420/4 Monthly Payment = [B]$105[/B]

Fred had 156 dollars to spend on 9 books. After buying them he had 12 dollars. How much did each book cost? Subtract the 12 dollars left over from the $156 starting amount: $156 - $12 = $144 Now divide $144 / 9 books to get the cost per book: $144/9 = [B]$16 per book[/B]

f^2+5g = 3md for d Divide each side by 3m to isolate d: (f^2+5g)/3m = 3md/3md Cancel the 3m on the right side and we get: d = [B](f^2+5g)/3m[/B]

Let g = Gary's pets and a = Abe's pets. We are given two equations: (1) g = a - 3 (2) a + g = 15 Substitute (1) into (2) a + (a - 3) = 15 Combine Like Terms: 2a - 3 = 15 Add 3 to each side: 2a = 18 Divide each side by 2 to isolate a: a = 9 --> Abe has 9 pets Substitute a = 9 into Equation (1) g = 9 - 3 g = 6 --> Gary has 6 pets

Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for the cut parts of pineapples. Take our whole pineapples divided by the number of equal parts: [B]7/4[/B]

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is the number? Let the number be n: [LIST] [*]n [*]Add 2: n + 2 [*]Divide the sum by 3: (n + 2)/3 [*]The word "gets" means an equation, so we set (n + 2)/3 equal to 7 [/LIST] (n + 2)/3 = 7 Cross multiply: n + 2 = 21 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B2%3D21&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]19[/B]

Given: 9 - 4x = -19 Prove: x = 7 Solve for [I]x[/I] in the equation 9 - 4x = - 19 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 9 and -19. To do that, we subtract 9 from both sides -4x + 9 - 9 = -19 - 9 [SIZE=5][B]Step 2: Cancel 9 on the left side:[/B][/SIZE] -4x = -28 [SIZE=5][B]Step 3: Divide each side of the equation by -4[/B][/SIZE] -4x/-4 = -28/-4 x = [B]7[/B]

gy=-g/v+w for g Multiply each side of the equation by v to eliminate fractions: gvy = -g + vw Add g to each side: gvy + g = -g + g + vw Cancel the g's on the right side and we geT: gvy + g = vw Factor out g on the left side: g(vy + 1) = vw Divide each side of the equation by (vy + 1): g(vy + 1)/(vy + 1) = vw/(vy + 1) Cancel the (vy + 1) on the left side and we geT: g = [B]vw/(vy + 1)[/B]

Half of ab Half means we divide by 2: [B]ab/2[/B]

half of c subtracted from the sum of a and b The sum of a and b: a + b half of c means we divide c by 2: c/2 half of c subtracted from the sum of a and b: [B]a + b - c/2[/B]

Half of the difference of a and b The difference of a and b is written as: a - b Half of the difference means we divide (a - b) by 2: [B](a - b)/2[/B]

half of the sum of 2p and q The sum of 2p and q means we add q to 2p: 2p + q Half of this means we divide the sum by 2: [B](2p + q)/2[/B]

half of z increased by 10 Half of z (means we divide z by 2) z/2 Increased by 10 means we add 10 [B]z/2 + 10[/B]

half the difference of x and 3 The difference of x and 3 means we subtract 3 from x: x - 3 half of the difference means we divide the difference by 2: [B](x - 3)/2[/B]

half the sum of the numbers s, t, and u The [I]sum [/I]of s, t, and u means we add all 3: s + t + u [I]Half[/I] the sum means we divide the sum by 2: [B](s + t + u)/2[/B]

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. Happy Paws Cost: C = 16 + 1.5h Woof Watchers: C = 11 + 2.75h Setup the equation where there costs are equal 16 + 1.5h = 11 + 2.75h Subtract 11 from each side: 5 + 1.5h = 2.75h Subtract 1.5h from each side 1.25h = 5 Divide each side by 1.25 [B]h = 4[/B]

How many 1/4 sheets are there in 5 sheets We divide 5 sheets by 1/4 sheets: 5/1/4 However, when we divide by a fraction, it's the same as multiplying by the reciprocal of the fraction: The reciprocal of 1/4 is 4/1, so we have: 5 * 4/1 = 20/1 = [B]20[/B]

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents? 200 nickels has a value of 200 * 0.05 = $10. Average value of coins is $10/200 = 0.05 Set up our average equation, where we have total value divided by total coins: (200 * 0.05 + 0.1d)/(200 + d) = 0.08 Cross multiply: 16 + 0.08d = 10 + 0.1d Using our [URL='http://www.mathcelebrity.com/1unk.php?num=16%2B0.08d%3D10%2B0.1d&pl=Solve']equation solver[/URL], we get: [B]d = 300[/B]

How many kobo are there in y naira? One naira is divided into [B]100 kobo[/B]. So we have [B]100y kobo[/B]

How much do 10 pieces of candy cost if 1000 pieces cost 100.00? Set up a proportion of pieces to cost 10/x = 1000/100 Divide the right side by 100 on top and bottom 10/x = 10/1 [B]x = 1[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 10 years? Assume the account earns 6% interest compounded monthly. We start with a balance of B. We want to know: B(1.06)^10 = 6000 B(1.79084769654) = 6000 Divide each side of the equation by 1.79084769654 to solve for B B = [B]3,350.37[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 8% interest compounded monthly. 8% compounded monthly = 8/12 = 0.6667% per month. 15 years = 15*12 = 180 months We want to know an initial balance B such that: B(1.00667)^180 = $6,000 3.306921B = $6,000 Divide each side by 3.306921 [B]B = $1,814.38[/B]

I grade 160 tests in 5 hours. How many tests do I grade per hour? 160 tests / 5 hours Divide top and bottom by 5: [B]32 tests per hour[/B]

6 cakes for 8 people. Divide by 8 people to get the cakes for each person. 6/8 cake per person. However, this fraction can be simplified. Divide the top and bottom by 2. We get 3/4, or 0.75 cake for each person.

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years have I been investing? Simple interest is calculated using interest * principal. We have 5% * 3000 = $150 interest per year We take our $600 of total interest and divide it by our interest per year to get the total years: $600 / $150 = [B]4 years[/B]

I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red. If have i 45 blankets, how many are blue? If 8 out of 15 blankets are red, then 15 - 8 = 7 are blue So 7 out of every 15 blankets are blue. Set up a proportion of blue blankets to total blankets where b is the number of blue blankets in 45 blankets 7/15 = b/45 Cross multiply: If 2 proportions are equal, then we can do the following: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 15b = 45 * 7 15b = 315 To solve for b, divide each side of the equation by 15: 15b/15 = 315/15 Cancel the 15's on the left side and we get: b = [B]21[/B]

If $9000 grows to $9720 in 2 years find the simple interest rate. Simple interest formula is Initial Balance * (1 + tn) = Current Balance We have [LIST] [*]Initial Balance = 9000 [*]Current Balance = 9720 [*]n = 2 [/LIST] Plugging in these values, we get: 9000 * (1 + 2t) = 9720 Divide each side by 9000 1 + 2t = 1.08 Subtract 1 from each sdie 2t = 0.08 Divide each side by 2 t = [B]0.04 or 4%[/B]

If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners and 2 walkers? [U]Set up a joint variation equation, for the 100 runners, 4 bicyclists, and 5 walkers:[/U] 100 = 4 * 5 * k 100 = 20k [U]Divide each side by 20[/U] k = 5 <-- Coefficient of Variation [U]Now, take scenario 2 to determine the bicyclists with 20 runners and 2 walkers[/U] 20 = 2 * 5 * b 20 = 10b [U]Divide each side by 10[/U] [B]b = 2[/B]

if 200 is divided in the ratio of 1:3:4 , what is the greatest number Determine the ratio denominator by adding up the ratio amounts: 1 + 3 + 4 = 8 So we have the following ratios and ratio amounts with our greatest number in bold: [LIST] [*]1/8 * 200 = 25 [*]3/8 * 200 = 75 [*]4/8 * 200 = [B]100[/B] [/LIST]

If 2x + y = 7 and y + 2z = 23, what is the average of x, y, and z? A. 5 B. 7.5 C. 15 D. 12.25 Add both equations to get all variables together: 2x + y + y + 2z = 23 + 7 2x + 2y + 2z = 30 We can divide both sides by 2 to simplify: (2x + 2y + 2z)/2= 30/2 x + y + z = 15 Notice: the average of x, y, and z is: (x + y + z)/3 But x + y + z = 15, so we have: 15/3 = [B]5, answer A[/B] [MEDIA=youtube]tOCAhhfMCLI[/MEDIA]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3 Take this in pieces, where "a number" means an arbitrary variable, let's call it "x". [LIST=1] [*]3 times a number --> 3x [*]3 times a number added to 2 --> 3x + 2 [*]The number plus 4 --> x + 4 [*]is divided by --> (3x + 2)/(x + 4) [*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3 [/LIST]

If 3(c + d) = 5, what is the value of c + d? A) 3/5 B) 5/3 C) 3 D) 5 Divide each side of the equation by 3 to [U]isolate[/U] c + d 3(c + d)/3 = 5/3 Cancel the 3's on the left side, we get: c + d = [B]5/3, or answer B[/B]

If 3/5 of a bun is shared equally between 4 people, what fraction of the bun would each receive? [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F5&frac2=1%2F4&pl=Multiply']We divide 3/5 by 4[/URL] to get [B]3/20[/B]

If 4x+7=xy-6, then what is the value of x, in terms of y Subtract xy from each side: 4x + 7 - xy = -6 Add 7 to each side: 4x - xy = -6 - 7 4x - xy = -13 Factor out x: x(4 - y) = -13 Divide each side of the equation by (4 - y) [B]x = -13/(4 - y)[/B]

if a+b=2 and a2-b2=-4, what is the value of a-b? a^2 - b^2 = -4 Factor this: (a + b)(a - b) = -4 We know from above, (a +b) = 2, so substitute: 2(a - b) = -4 Divide each side by 2 [B](a - b) = -2[/B]

if a divides b, then a divides bc Suppose a divides b. Then there exists an integer q such that b = aq, so that bc = a(qc) and a divides bc. Suppose that a divides c. Then there exists an integer k such that c = ak, so that bc = a(kb) and a divides bc.

If a number is increased by 16 and then divided by 3, the result is 8. Let x be the number. We have: (x + 16)/3 = 8 Cross multiply x + 16 = 24 Using our equation calculator, we get: [B]x = 8[/B]

If a pound of coffee costs $4, how many ounces can be bought for $1.80 Using our conversion calculator, we find [URL='https://www.mathcelebrity.com/weightcon.php?quant=1&pl=Calculate&type=pound']1 pound [/URL]= 16 ounces $4 per 16 ounces = 4/16 [URL='https://www.mathcelebrity.com/perc.php?num=4&den=16&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']We can simplify this fraction[/URL] to 0.25 per ounce We take our 1.80 divided by 0.25 per ounce 1.80/0.25 = [B]7.2 ounces of coffee [MEDIA=youtube]5eZAav1drX0[/MEDIA][/B]

If c=3 and d=4 evaluate cd divided by 2 cd = 3(4) cd = 12 Divide this by 2: 12/2 [B]6[/B]

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and distance? Divide each side by S to isolate T: D/S = S x T/S Cancel the S's on the right side: [B]T = D/S[/B]

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG? By segment addition, we know that: EF + FG = EG Substituting in our values for the 3 segments, we get: 9x - 17 + 17x - 14 = 20x + 17 Group like terms and simplify: (9 + 17)x + (-17 - 14) = 20x - 17 26x - 31 = 20x - 17 Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides 26x - 31 - 20x = 20x - 17 - 20x [SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE] 6x - 31 = -17 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -31 and -17. To do that, we add 31 to both sides 6x - 31 + 31 = -17 + 31 [SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE] 6x = 14 [SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE] 6x/6 = 14/6 x = [B]2.3333333333333[/B]

If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10 [U]Evaluate f(g(x))[/U] f(g(x)) = 3(x^2 + 2x) + 1 f(g(x)) = 3x^2 + 6x + 1 [U]When f(g(x)) = 10, we have[/U] 10 = 3x^2 + 6x + 1 [U]Subtract 10 from each side:[/U] 3x^2 + 6x - 9 = 0 Divide each side of the equation by 3 x^2 + 2x - 3 = 0 Factor, we have: (x + 3)(x - 1) = 0 So x is either [B]1 or -3[/B]

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have? Let h = Mr. Hernandez's students and d = Mr. Daniels students. We are given two equations: (1) h = 5d (2) d + h = 150 Substitute equation (1) into equation (2) d + (5d) = 150 Combine like terms: 6d = 150 Divide each side of the equation by 6 to isolate d d = 25 <-- Mr. Daniels Students Now, plug the value for d into equation (1) h = 5(25) h = 125 <-- Mr. Hernandez students

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2. We set up the variation equation with a constant k such that: p = k/q^2 [I](inversely proportional means we divide) [/I] When q is 4 and p is 2, we have: 2 = k/4^2 2 = k/16 Cross multiply: k = 2 * 16 k = 32 Now, the problem asks for p when q = 2: p = 32/2^2 p = 32/4 p = [B]8 [MEDIA=youtube]Mro0j-LxUGE[/MEDIA][/B]

If tanx = 3/4 ,what is cosx? tan(x) = sin(x)/cos(x), so we have: sin(x)/cos(x) = 3/4 cross multiply: 4sin(x) = 3cos(x) Divide each side by 3 to isolate cos(x): cos(x) = [B]4sin(x)/3 [/B]

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi C = 2pir, so we have: C = 16? 16? = 2?r Divide each side by 2?: r = 16?/2? r = 8 Now, the area of a circle A is denoted below: A = ?r^2 Given r = 8 from above, we have: A = ?(8)^2 A = [B]64?[/B]

Let a be the cost of the ball and b be the cost of the bat: We're given 2 equations: [LIST=1] [*]a + b = 1.10 [*]b = a + 1 [/LIST] Substitute equation (2) into equation (1) for b: a + a + 1 = 1.10 Combine like terms: 2a + 1 = 1.10 Subtract 1 from each side: 2a + 1 - 1 = 1.10 - 1 2a = 0.10 Divide each side by 2: 2a/2 = 0.10/2 a = [B]0.05[/B] [MEDIA=youtube]79q346Hy7R8[/MEDIA]

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y? Set up our given ratio: 2x/5y = 3/4 Cross multiply: 2x * 4 = 5y * 3 8x = 15y Divide each side by 8: 8x/8 = 15y/8 x = 15y/8 Now divide each side by y to find x/y: x/y = 15y/8y x/y =[B] 15/8[/B]

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially. We know from the distance formula (d) using rate (r) and time (t) that: d = rt Regular speed: 1200 = rt Divide each side by t, we get: r = 1200/t Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3 3600 = (r - 40)(t + 1/3) If we multiply 3 by (t + 1/3), we get: 3t + 1 So we have: 3600 = (r - 40)(3t + 1) Substitute r = 1200/t into the reduced speed equation: 3600 = (1200/t - 40)(3t + 1) Multiply through and we get: 3600 = 3600 - 120t + 1200/t - 40 Subtract 3,600 from each side 3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40 The 3600's cancel, so we get: - 120t + 1200/t - 40 = 0 Multiply each side by t: -120t^2 - 40t + 1200 = 0 We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get: t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is: [B]t = 3[/B]

If twice a number is divided by 7, the result is -28. The phrase [I]a number[/I] means an arbitrary variable, let's call it "x". Twice x means we multiply x by 2: 2x Divide this by 7: 2x/7 We set this equal to -28, and we have our algebraic expression: [B]2x/7 = -28 [/B]

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers? Let the smaller number be n. The next consecutive even number is n + 2. Add them together to equal 226: n + n + 2 = 226 Solve for [I]n[/I] in the equation n + n + 2 = 226 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1)n = 2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2n + 2 = + 226 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 2 and 226. To do that, we subtract 2 from both sides 2n + 2 - 2 = 226 - 2 [SIZE=5][B]Step 4: Cancel 2 on the left side:[/B][/SIZE] 2n = 224 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 224/2 n = [B]112 [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B2%3D226&pl=Solve']Source[/URL][/B]

If x is divided by 9, the remainder is 5. What is the remainder if 3x is divided by 9? pick an integer x where when dividing by 9, we get a remainder of 5. 14/9 gives us a remainder of 5. Now multiply 14 by 3: 14 * 3 = 42 [URL='https://www.mathcelebrity.com/modulus.php?num=42mod9&pl=Calculate+Modulus']42/9 gives a remainder of[/URL] [B]6[/B]

If x/2y = 3/4, what is the value of y/x? Cross multiply this proportion: 4x = 3(2y) 4x = 6y Divide each side by x: 4x/x = 6y/x The x's cancel, and we have: 6y/x = 4 Divide each side by 6: 6y/6x = 4/6 The 6's on the left cancel, we have: y/x = 4/6 We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']Type in Simplify 4/6 into the search engine[/URL], and we get 2/3. y/x = [B]2/3[/B]

if x^2=y^3, for what value of z does x^{3z}= y^9 y^9 = y^3 * y^3, so if we square the right side, we must square the left side for equivalence: x^2 * x^2 = x^4 Therefore, x^4 = y^9 Going back to our problem, x^{3z}= y^9, so 3z = 4 Divide each side by 3 to isolate z, and we have: 3z/3 = 4/3 z = [B]4/3[/B]

If y varies directly as x and inversely as z, then which equation describes the relation? Directly means we multiply, inversely means we divide, so we have a constant k such that: [B]y = kx/z[/B]

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box. Set up a proportion of dollars to boxes where b is the number of boxes for $4: 6/1/3 = 4/b Cross multiply: 6b = 4/3 Multiply each side by 1/6 to isolate b: b = 4/18 [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=18&num3=&pl=GCF+and+LCM']Type in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2. Divide 4 and 18 in the fraction by 2. We get the reduced fraction of: [B]b = 2/9[/B]

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brothers age? Let b be the brother's age. We're given the following relationship for the brother's age and my age: b/3 + 20 = 31 Subtract 20 from each side: b/3 + 20 - 20 = 31 - 20 Cancel the 20's on the left side and we get: b/3 = 11 Cross multiply, and we get: b = 3 * 11 b = [B]33 [/B] Check our work using b = 33 for b/3 + 20 = 31: 33/3 + 20 ? 31 11 + 20 ? 31 31 = 31

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age right now be b. We have, in 16 years, Ben's age will be 3 times what his age is now: b + 16 = 3b Subtract b from each side: 2b = 16 Divide each side by 2 [B]b = 8[/B] Check our work: 16 years from now, Ben's age is 8 + 16 = 24 And, 8 x 3 = 24

In 45 years, Gabriela will be 4 times as old as she is right now. Let a be Gabriela's age. we have: a + 45 = 4a Subtract a from each side: 3a = 45 Divide each side by a [B]a = 15[/B]

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: [LIST] [*]Let b be the number of boys [*]Let g be the number of girls [/LIST] We're given two equations: [LIST=1] [*]b = g + 5 [*]b + g = 13 [/LIST] Substitute equation (1) for b into equation (2): g + 5 + g = 13 Grouping like terms, we get: 2g + 5 = 13 Subtract 5 from each side: 2g + 5 - 5 = 13 - 5 Cancel the 5's on the left side and we get: 2g = 8 Divide each side of the equation by 2 to isolate g: 2g/2 = 8/2 Cancel the 2's on the left side and we get: g = 4 Substitute g = 4 into equation (1) to solve for b: b = 4 + 5 b = [B]9[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 40% to 77 in 2012 from 2011. How many robberies were there in Springfield in 2011? Let r be the number of robberies in 2011. We have: Robberies in 2012 = Robberies in 2011 * 1.4 77 = r * 1.4 Divide each side by 1.4 [B]r = 55[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? Let w be the winning team's points, and l be the losing team's points. We have two equations: [LIST=1] [*]w + l = 41 [*]w - l = 27 [/LIST] Add the two equations: 2w = 68 Divide each side by 2 [B]w = 34[/B] Substitute this into (1) 34 + l = 41 Subtract 34 from each side [B]l = 7[/B] Check your work: [LIST=1] [*]34 + 7 = 41 <-- check [*]34 - 7 = 27 <-- check [/LIST] The final score of the game was [B]34 to 7[/B]. You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980? Age in 1980: [LIST] [*]Let Michael's age be m [*]Nancy's age is 2m [*]Rick's age is 2 * 2m = 4m [/LIST] Age in 1992: [LIST] [*]Michael's age = m + 12 [*]Nancy's age is 2m + 12 [*]Rick's age is 2 * 2m = 4m + 12 [/LIST] Total them up: m + 12 + 2m + 12 + 4m + 12 = 78 Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78 [SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE] (1 + 2 + 4)m = 7m [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 12 + 12 + 12 = 36 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 7m + 36 = + 78 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 36 and 78. To do that, we subtract 36 from both sides 7m + 36 - 36 = 78 - 36 [SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE] 7m = 42 [SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE] 7m/7 = 42/7 m = 6 Rick's age = 6 * 4 = [B]24 [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B12%2B2m%2B12%2B4m%2B12%3D78&pl=Solve']Source[/URL] [/B]

In this class of 4/5 students are right handed. if there are 20 right handed students, what is the total number of students in this class? Let x be the total number of students in the class. We have: 4/5x = 20 Cross multiplying or using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%3D100&pl=Solve']equation calculator[/URL], we get: 4x = 100 Divide each side by 4 [B]x = 25[/B]

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls? Rate * Time = Output Let "Rate" (r) be the rate at which [B]one person[/B] works. So we have: 7r * 60 = 5 Multiply through and simplify: 420r = 5 Divide each side by 5 to isolate r: r = 1/84 So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate: 10rt = 10 With r = 1/84, we have: 10t/84 = 10 Cross multiply: 10t = 840 To solve for t, we t[URL='https://www.mathcelebrity.com/1unk.php?num=10t%3D840&pl=Solve']ype this equation into our search engine[/URL] and we get: t = [B]84 minutes[/B]

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets Let a = Number of adult tickets and c be the number of child tickets. [LIST=1] [*]7a + 4c = 40 [*]a + c = 7 [*]Rearrange (2): a = 7 - c [/LIST] Now substitute a in (3) into (1): 7(7 - c) + 4c = 40 49 - 7c + 4c = 40 49 - 3c = 40 Add 3c to each side and subtract 40: 3c = 9 Divide each side by 3: [B]c = 3 [/B] Substitute c = 3 into Equation (2) a + 3 = 7 Subtract 3 from each side: [B]a = 4[/B]

Jack is making snack bags. He has 18 baby carrots and 42 pretzels. He wants to divide them equally among the bags. What is the greatest number of snack bags he can make? Find the [URL='http://www.mathcelebrity.com/gcflcm.php?num1=18&num2=42&num3=&pl=GCF']Greatest Common Factor[/URL] of (18, 42) = 6 6 bags for 18 carrots = 3 carrots per bag 6 bags for 42 pretzels = 7 pretzels per bag [B]6 bags is the answer[/B]

Jake used 5 boxes to pack 43.5 kg of books. If the boxes each weighed the same and held 8 books, what did each book weigh? [U]Set up equations were w is the weight of each book:[/U] [LIST=1] [*]5 boxes * 8 books * w = 43.5 [*]40w = 43.5 [/LIST] [U]Divide each side by 40[/U] [B]w = 1.0875 kg[/B]

James is ordering action figures online. Each action figure is $9. Shipping cost $10 per order. James does not want to spend over $154. How many action figures can he order? Step 1: Subtract the cost of shipping from the spend $154 - $10 = $144 Step 2: Divide $144 to spend after shipping by $9 action figures 144/9 = [B]$16 action figures[/B]

Jamie spent $15.36 on several items at the store. he spent an equal amount on each item. if jamie spent $1.92 on each item, how many items did he buy? Let x equal the number of items Jamie bought. We have: 1.92x = 15.36 Divide each side by 1.92 [B]x = 8[/B]

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy. Let s be the number of sodas. Cost for the day is: Price per soda * s + Admission Price 4.25s + 42 We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55 [B]4.25s + 42 <= 55[/B] [B][/B] If the problems asks you to solve for s, we type it in our math engine and we get: Solve for [I]s[/I] in the inequality 4.25s + 42 ? 55 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 42 and 55. To do that, we subtract 42 from both sides 4.25s + 42 - 42 ? 55 - 42 [SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE] 4.25s ? 13 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE] 4.25s/4.25 ? 13/4.25 [B]s ? 3.06[/B]

Jane is twice a old as Joel. If their ages total 63, how old is Joel? Joel = j Jane = 2j j + 2j = 63 3j = 63 Divide each side by 3: 3j/3 = 63/j Cancel the 3's on the left side: j = [B]21[/B]

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling? Distance = Rate * Time We're given D = 395 and t = 5 We want Rate. We divide each side of the equation by time: Distance / Time = Rate * Time / Time Cancel the Time's on each side and we get: Rate = Distance / Time Plugging our numbers in, we get: Rate = 395/5 Rate = [B]79 kilometers[/B]

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have? Let the number of nickels be n Let the number of dimes be d We're given two equations: [LIST=1] [*]d = n [*]0.05n + 0.1d = 2.25 [/LIST] Substitute equation (1) for d into equation (2): 0.05n + 0.1n = 2.25 Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (0.05 + 0.1)n = 0.15n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.15n = + 2.25 [SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE] 0.15n/0.15 = 2.25/0.15 n = [B]15[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.1n%3D2.25&pl=Solve']Source[/URL]

[SIZE=6]Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour. How long does it take Joe to catch Jason? A. 3 hours B. 4 hours C. 6 hours D. 8 hours Distance formula is d = rt Jason's formula (Add 9 since he's ahead 9 miles): d = 5.5t + 9 Joe's formula: d = 7t Set both distance formulas equal to each other: 5.5t + 9 = 7t Subtract 5.5t from each side: 5.5t - 5.5t + 9 = 7t - 5.5t 1.5t = 9 Divide each side by 1.5: 1.5t/1.5 = 9/1.5 t = [B]6 hours[/B] [U]Check our work with t = 6[/U] Joe = 7(6) = 42 Jason = 5.5(6) + 9= 33 + 9 = 42 [MEDIA=youtube]qae3WCq9wzM[/MEDIA] [/SIZE]

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar. with a ticket price of t, we have the total cost written as: 1.04 * (7*4 + 4t)= 407.68 Divide each side by 1.04 1.04 * (7*4 + 4t)/1.04= 407.68/1.04 Cancel the 1.04 on the left side and we get: 7*4 + 4t = 392 28 + 4t = 392 To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=28%2B4t%3D392&pl=Solve']type it in our math engine[/URL] and we get: t = [B]91[/B]

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? [U]Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations:[/U] (1) b + j = 25 (2) j = b + 5 [U]Substitute (2) into (1)[/U] b + (b + 5) = 25 [U]Group the b terms[/U] 2b + 5 = 25 [U]Subtract 5 from each side[/U] 2b = 20 [U]Divide each side by b[/U] [B]b = 10 [/B] [U]Substitute b = 10 into (2)[/U] j = 10 + 5 [B]j = 15[/B]

Jill made 122 muffins. She put them into 3 boxes and has two muffins left. How many are in each box if they all contain the same amount of muffins? Let m equal the number of muffins per box. We're told that we have 3 boxes and 2 muffins left after filling up all 3 boxes. 3m + 2 = 122 To solve for m, we subtract 2 from each side: 3m + 2 - 2 = 122 - 2 Cancel the 2's on the left side and we get: 3m = 120 Divide each side by 3 to isolate m: 3m/3 = 120/3 Cancel the 3's on the left side and we get: m = [B]40[/B]

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number? Start with x. Add 20 to it x + 20 Double it 2(x + 20) Set this equal to 99.2 2(x + 20) = 99.2 Divide each side by 2: x + 20 = 49.6 Subtract 20 from each side: x = [B]29.6[/B]

John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane? John's red ratio = 18/30 Using a [URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=30&num3=&pl=GCF+and+LCM']GCF for (18, 30)[/URL], we get 6. Divide top and bottom of 18/30 by 6, we get 3/5 John's blue ratio is 12/30 Using a [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=30&num3=&pl=GCF']GCF of (12, 30)[/URL], we get 6. Divide top and bottom of 12/30 by 6, we get 2/5 Use these same ratios for Jane, we get: Red: 3(20)/5 = 12 Blue: 20 - 12 = 8 Now the problem asks how many more blue marbles John has then Jane. We have 12 - 8 = [B]4[/B].

John need 250 hours of community service. He volunteers 2 days a week for 4 hours. How long will it take John to reach 250 hours? Each week, John serves 2 days * 4 hours per day = 8 hours. We divide 250/8 to get [B]31.25 weeks[/B].

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

joseph buys 3 1/2 pounds of hamburger. how many quarter -pound can he make? A quarter pound is 1/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%261%2F2&frac2=3%2F8&pl=Simplify']3 & 1/2[/URL] = 7/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F2&frac2=1%2F4&pl=Divide']7/2 / 1/4[/URL] = [B]14 quarter pounders[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out? Let m be the number of messages. We have a cost function of: C(m) = 9 + 0.1(m - 600) We are given C(m) = 18.20 18.20 = 9 + 0.1(m - 600) 18.20 = 9 + 0.1m - 60 Combine like terms: 18.20 = 0.1m - 51 Add 51 to each side 0.1m = 69.20 Divide each side by 0.1 [B]m = 692[/B]

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers? Let's compare based on correct answers to questions: Juliana = 42/80 = 0.525 Angela = 21/40 = 0.525 So yes, they do have the same portion of correct answers. But there's another way to solve this: [LIST=1] [*]Divide Juliana's the top and bottom of Juliana's fraction by 2. [*]We picked 2 as a GCF shown in our calculator. [*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL]. [/LIST] Divide top and bottom of Juliana's fraction by the GCF of 2 42/2 = 80/2 = 21/40 This ratio equals Angela's.

K varies inversely with square root of m and directly with the cube of n. [LIST] [*]We take a constant c as our constant of proportionality. [*]The word inversely means we divide [*]The word directly means we multiply [/LIST] [B]k = cn^3/sqrt(m)[/B]

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible numbers of times that she can play? [U]Let x = the number of games Karin can play with her money[/U] 0.5x = 3 [U]Divide each side by 0.5[/U] [B]x = 6[/B]

Let k = Katie's age and m = Mara's age. We have 2 equations: (1) k = 2m (2) k + m = 24 Substitute (1) into (2) (2m) + m = 24 Combine like terms: 3m = 24 Divide each side of the equation by 3 to isolate m m = 8 If m = 8, substituting into (1) or (2), we get k = 16. [MEDIA=youtube]Cu7gSgNkQPg[/MEDIA]

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Let t = number of 20 bills and f = number of 50 bills. We have two equations. (1) 20t + 50f = 390 (2) t + f = 15 [U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U] (3) t = 15 - f [U]Now substitute (3) into (1)[/U] 20(15 - f) + 50f = 390 300 - 20f + 50f = 390 [U]Combine f terms[/U] 300 + 30f = 390 [U]Subtract 300 from each side[/U] 30f = 90 [U]Divide each side by 30[/U] [B]f = 3[/B] [U]Substitute f = 3 into (3)[/U] t = 15 - 3 [B]t = 12[/B]

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class? The percentage equals hours spent on statistics divided by total hours spent studying for everything. [U]Calculate total study hours:[/U] Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours Total Study Hours = 10 + 8 + 12 Total Study Hours = [B]30[/B] [U]Calculate Statistics Study Hours Percentage:[/U] Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours Statistics Class Study Hours = 8/30 Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']fraction to decimal calculator[/URL], we get Statistics Class Study Hours = [B]26.67%[/B]

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers Declare Variables for each number: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 12 [*]l + s = 74 [/LIST] Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l: s + 12 + s = 74 Solve for [I]s[/I] in the equation s + 12 + s = 74 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (1 + 1)s = 2s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2s + 12 = + 74 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 12 and 74. To do that, we subtract 12 from both sides 2s + 12 - 12 = 74 - 12 [SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE] 2s = 62 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2s/2 = 62/2 s = [B]31[/B] To solve for l, we substitute in s = 31 into equation (1): l = 31 + 12 l = [B]43[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 4 [*]l + s = 40 [/LIST] To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l. Subtract 4 from each side in equation (1) l - 4 = s + 4 - 4 Cancel the 4's and we get: s = l - 4 Our given equations are now: [LIST=1] [*]s = l - 4 [*]l + s = 40 [/LIST] Substitute equation (1) into equation (2) for s: l + l - 4 = 40 Grouping like terms for l, we get: 2l - 4 = 40 Add 4 to each side: 2l - 4 + 4 = 40 + 4 Cancelling the 4's on the left side, we get 2l = 44 Divide each side of the equation by 2 to isolate l: 2l/2 = 44/2 Cancel the 2's on the left side and we get: l = [B]22[/B]

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing. Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.) Feet of fencing = n Perimeter of square garden = n Each side of square = n/4 Square garden's area = (n/4)^2 = n^2/16 Area of circle garden with circumference = n is: Circumference = pi * d n = pi * d Divide body tissues by pi: d = n/pi Radius = n/2pi Area = pi * n/2pi * n/2pi Area = pin^2/4pi^2 Reduce by canceling pi: n^2/4pi n^2/4 * 3.14 n^2/12.56 The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet. Area of Circle - Area of Square = 1380 n^2/12.56 - n^2/16 = 1380 Common denominator = 200.96 (16n^2 - 12.56n^2)/200.96 = 1380 3.44n^2/200.96 = 1380 Cross multiply: 3.44n^2 = 277,324.8 n^2 = 80,617.7 n = 283.9 Nearest foot = [B]284[/B]

Laura spent half of her money on a necklace. She spent 14.60 of what was left having dinner with carolyn. if she had 3.90 left, how much money did she start out with? Let x equal Laura's starting money 1/2x = 14.60 + 3.90 1/2x = 18.5 Divide each side by 1/2 [B]x = $37[/B]

Laura weighs 45 pounds more than her pet dog. When they are on the scale together, they weigh 85 pounds. How much does Laura weigh? Let Laura weigh l and her dog weigh d. WE have: [LIST=1] [*]l = d + 45 [*]d + l = 85 [/LIST] Substitute equation (1) into Equation (2) for l: d + d + 45 = 85 Solve for [I]d[/I] in the equation d + d + 45 = 85 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 1)d = 2d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2d + 45 = + 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 45 and 85. To do that, we subtract 45 from both sides 2d + 45 - 45 = 85 - 45 [SIZE=5][B]Step 4: Cancel 45 on the left side:[/B][/SIZE] 2d = 40 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2d/2 = 40/2 d = 20 From equation (1), we substitute d = 20: l = d + 45 l = 20 + 45 l = [B]65 pounds [URL='https://www.mathcelebrity.com/1unk.php?num=d%2Bd%2B45%3D85&pl=Solve']Source[/URL][/B]

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates. 6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate Set up equation using h hours: 3h = 9 Divide each side by 3 [B]h = 3[/B]

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer? For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6 Let t = tens digit and o = ones digit P(n) = to S(n) = t + o P(n) + S(n) = to + t + o N = 10t + o Set them equal to each other N = P(N) + S(N) 10t + o = to + t + o o's cancel, so we have 10t = to + t Subtract t from each side, we have 9t = to Divide each side by t o = 9 So any two-digit number with 9 as the ones digit will work: [B]{19,29,39,49,59,69,79,89,99}[/B]

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have? [U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U] (1) d + p = 47 (2) 0.1d + 0.01p = 2.18 [U]Rearrange (1) into (3) by solving for d[/U] (3) d = 47 - p [U]Substitute (3) into (2)[/U] 0.1(47 - p) + 0.01p = 2.18 4.7 - 0.1p + 0.01p = 2.18 [U]Group p terms[/U] 4.7 - 0.09p = 2.18 [U]Add 0.09p to both sides[/U] 0.09p + 2.18 = 4.7 [U]Subtract 2.18 from both sides[/U] 0.09p = 2.52 [U]Divide each side by 0.09[/U] [B]p = 28[/B] [U]Now substitute that back into (3)[/U] d =47 - 28 [B]d = 19[/B]

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt? Let Dan's debt be d. Let Luke's debt be l. We're given two equations: [LIST=1] [*]d + l = 72 [*]l = 3d [/LIST] Substitute equation (2) for l into equation (1): d + 3d = 72 Solve for [I]d[/I] in the equation d + 3d = 72 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 3)d = 4d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 4d = + 72 [SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE] 4d/4 = 72/4 d = [B]18[/B]

M is halved, then 7 is added Take this algebraic expression in parts: [LIST] [*]M is halved. This means we divide M by 2: M/2 [*]Then 7 is added. We add 7 to M/2 [/LIST] [B]M/2 + 7[/B]

M is the sum of a and its reciprocal The reciprocal of a variable is 1 divided by the variable 1/a The sum of a and its reciprocal means we add: a + 1/a The phrase [I]is[/I] means an equation, so we set M equal to the sum of a + 1/a: [B]M = 1 + 1/a[/B]

m=u/k-r/k for k Multiply both sides by k to eliminate the k denominator: km = uk/k - rk/k Cancel the k's on the right side and we get km = u - r Divide each side by m: km/m = (u - r)/m Cancel the m on the left side: [B]k = (u - r)/m[/B]

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece? A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches. Area of a circle is pi(r^2). With r = 7, we have: A =7^2(pi) A = 49pi Area of a slice of pizza is the area of the full pizza divided by 8 A(Slice) = [B]49pi/8[/B]

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How many hours does Margaret work each week? Let h be the hours worked We know that hourly rate * h equals total earnings. The phrases at least and no more than signify inequalities, so we have: 450 <= 15h <= 600 Divide each entry by 15: [B]30 <= h <= 40[/B] This means Margaret works at least 30 hours a week and no more than 40

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start? Let the number of boxes Maria started with be b. We're given the following pieces: [LIST] [*]She starts with b [*]She bought 7 boxes. So we add 7 to b: b + 7 [*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2 [*]Only 22 boxes left means we set (b + 7)/2 equal to 22 [/LIST] (b + 7)/2 = 22 Cross multiply: b + 7 = 22 * 2 b + 7 = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get: b = [B]37[/B]

Let n be the number of nickels and q be the number of quarters. We have two equations: (1) n + q = 24 (2) 0.05n + 0.25q = 3 Rearrange (1) to solve for n in terms of q for another equation (3) (3) n = 24 - q Plug (3) into (2) 0.05(24 - q) + 0.25q = 3 Multiply through: 1.2 - 0.05q + 0.25q = 3 Combine q terms 0.2q + 1.2 = 3 Subtract 1.2 from each side: 0.2q = 1.8 Divide each side by 0.2 [B]q = 9[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.

Volume of rectangular prism is: V = lwh Plugging in the numbers you gave: 195 = (6)(5)h 195 = 30h Divide each side by 30 h = 6.5 6.5 feet is 6 feet, 6 inches. This is 2 inches more than your actor, so [B]yes[/B], he will fit in the box standing up.

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve and inequality to find how many hours she will need to babysit to buy the dress. Subtract remaining amount needed after savings: 112 - 40 = 72 Let h be her hourly wages for babysitting. We have the equation: [B]9h = 72[/B] Divide each side by 9 [B]h = 8[/B]

Matthew's cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the weight of all three pets is 35 pounds, ow much does his hamster weigh? Setup weights and relations: [LIST] [*]Hamster weight: w [*]Cat weight: w + 10 [*]Dog weight:w + 10 [/LIST] Add all the weights up: w + w + 10 + w + 10 = 35 Solve for [I]w[/I] in the equation w + w + 10 + w + 10 = 35 [SIZE=5][B]Step 1: Group the w terms on the left hand side:[/B][/SIZE] (1 + 1 + 1)w = 3w [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 10 + 10 = 20 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 3w + 20 = + 35 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants 20 and 35. To do that, we subtract 20 from both sides 3w + 20 - 20 = 35 - 20 [SIZE=5][B]Step 5: Cancel 20 on the left side:[/B][/SIZE] 3w = 15 [SIZE=5][B]Step 6: Divide each side of the equation by 3[/B][/SIZE] 3w/3 = 15/3 w =[B] 5[/B] [B] [URL='https://www.mathcelebrity.com/1unk.php?num=w%2Bw%2B10%2Bw%2B10%3D35&pl=Solve']Source[/URL][/B]

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink? [U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U] Max: 2b + 2d = 5 Bob: 3b + d = 5.50 [U]Rearrange Bob's equation by subtracting 3b from each side[/U] (3) d = 5.50 - 3b [U]Now substitute that d equation back into Max's Equation[/U] 2b + 2(5.50 - 3b) = 5 2b + 11 - 6b = 5 [U]Combine b terms:[/U] -4b + 11 = 5 [U]Subtract 11 from each side[/U] -4b = -6 [U]Divide each side by -4[/U] b = 3/2 [B]b = $1.50[/B] [U]Now plug that back into equation (3):[/U] d = 5.50 - 3(1.50) d = 5.50 - 4.50 [B]d = $1.00[/B]

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad? Let Max's father be age f. We're given: (f + 2)/4 = 13 Cross Multiply: f + 2 = 52 [URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get: f = [B]50[/B]

We need the speed of KM per hour. 25.6 km / 4 hours [U]Divide top and bottom by 4 to get km per hour[/U] [B]6.4km per hour[/B]

Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes did each of them sell? Let m = Michelle's cupcakes and j = Julie's cupcakes. We have two equations: m + j = 65 j = m + 9 Substituting, we get: m + (m + 9) = 65 Combine like terms, we get: 2m + 9 = 65 Subtract 9 from each side: 2m = 56 Divide each side by 2 to isolate m m = 28 If m = 28, then j = 28 + 9 = 37 So (m, j) = (28, 37)

Free Monomials Calculator - This calculator will raise a monomial to a power,multiply monomials, or divide monomials.

Mr. Vukovic is making pasta. He makes 3 � cups of pasta. How many � cup servings can Mr. Vukovic serve 3 & 1/2 = 7/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%261%2F2&frac2=3%2F4&pl=Divide']7/2 /3/4[/URL] = 14/3 = 4 & 2/3

Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Let x = Mr. Winkle downloads and y = Mrs. Winkle downloads. We then have x = y + 34 and x + y = 220. Substitute equation 1 into equation 2, we have: (y + 34) + y = 220 2y + 34 = 220 Subtract 34 from each side: 2y = 186 Divide each side by 2: y = 93 (Mrs. Winkle) x = 93 + 34 x = 127 (Mr. Winkle)

Take the number being multiplied by 5. Divide it in half Add a zero 14 * 5 Divide 14/2 = 7 Add a 0 --> 70 [MEDIA=youtube]lOJmx0Ygpz8[/MEDIA]

mx=ac/np for n Cross multiply: mnpx = ac Divide each side by mpx: mnpx/mpx = ac/mpx Cancel the mpx on the right side: n = [B]ac/mpx[/B]

n + .07n = $90.95 Group like terms: 1.07n = $90.95 Solve for [I]n[/I] in the equation 1.07n = 90.95 [SIZE=5][B]Step 1: Divide each side of the equation by 1.07[/B][/SIZE] 1.07n/1.07 = 90.95/1.07 n = [B]85 [URL='https://www.mathcelebrity.com/1unk.php?num=1.07n%3D90.95&pl=Solve']Source[/URL][/B]

n + 2n + 3n + 4n = 2 + 3 + 4 + 5 + 6 Solve for [I]n[/I] in the equation n + 2n + 3n + 4n = 2 + 3 + 4 + 5 + 6 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 2 + 3 + 4)n = 10n [SIZE=5][B]Step 2: Group the constant terms on the right hand side:[/B][/SIZE] 2 + 3 + 4 + 5 + 6 = 20 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 10n = + 20 [SIZE=5][B]Step 4: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 20/10 n = [B]2[/B]

n + 9n - 8 - 5 = 2n + 3 Solve for [I]n[/I] in the equation n + 9n - 8 - 5 = 2n + 3 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 9)n = 10n [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] -8 - 5 = -13 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 10n - 13 = 2n + 3 [SIZE=5][B]Step 4: Group variables:[/B][/SIZE] We need to group our variables 10n and 2n. To do that, we subtract 2n from both sides 10n - 13 - 2n = 2n + 3 - 2n [SIZE=5][B]Step 5: Cancel 2n on the right side:[/B][/SIZE] 8n - 13 = 3 [SIZE=5][B]Step 6: Group constants:[/B][/SIZE] We need to group our constants -13 and 3. To do that, we add 13 to both sides 8n - 13 + 13 = 3 + 13 [SIZE=5][B]Step 7: Cancel 13 on the left side:[/B][/SIZE] 8n = 16 [SIZE=5][B]Step 8: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 16/8 n = [B]2[/B]

n + 9n - 90 = 0 Solve for [I]n[/I] in the equation n + 9n - 90 = 0 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 9)n = 10n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 10n - 90 = [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -90 and 0. To do that, we add 90 to both sides 10n - 90 + 90 = 0 + 90 [SIZE=5][B]Step 4: Cancel 90 on the left side:[/B][/SIZE] 10n = 90 [SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 90/10 n = [B]9[/B]

n + n/2 + n/4 + n/8 + n/16 = 19,375 Convert to like fractions with a denominator of 16: 16n/16 + 8n/16 + 4n/16 + +2n/16 + n/16 = 19,375 31n/16 = 19,375 Cross multiply: 31n = 19,375 * 16 31n = 310000 Divide each side by 1: 31n/31 = 310000/31 n = [B]10,000[/B]

n = 3n - 1/2 Solve for [I]n[/I] in the equation n = 3n - 1/2 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 3n. To do that, we subtract 3n from both sides n - 3n = 3n - 0.5 - 3n [SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE] -2n = -0.5 [SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = -0.5/-2 n = [B]0.25 or 1/4[/B]

n = 5m^2d for d Divide each side by 5m^2 to isolate d: n/5m^2 = 5m^2d/5m^2 Cancel the 5m^2 on the right side and we get: d = [B]n/5m^2[/B]

n = b + d^2a for a Let's start by isolating the one term with the a variable. Subtract b from each side: n - b = b - b + d^2a Cancel the b terms on the right side and we get: n - b = d^2a With the a term isolated, let's divide each side of the equation by d^2: (n - b)/d^2 = d^2a/d^2 Cancel the d^2 on the right side, and we'll display this with the variable to solve on the left side: a = [B](n - b)/d^2 [MEDIA=youtube]BCEVsZmoKoQ[/MEDIA][/B]

n=i*x+y for i This is a literal equation. Subtract y from each side of the equation: n - y = i*x + y - y The y's cancel on the right side, so we have: n - y = ix Divide each side of the equation by x, to isolate i (n - y)/x = ix/x The x's cancel on the right side, so we have: i = [B](n - y)/x[/B]

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter? Declare variables for each age: [LIST] [*]Let Nancy's age be n [*]Let her daughter's age be d [/LIST] We're given two equations: [LIST=1] [*]n = 3d - 10 [*]n = 41 [/LIST] We set 3d - 10 = 41 and solve for d: Solve for [I]d[/I] in the equation 3d - 10 = 41 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 41. To do that, we add 10 to both sides 3d - 10 + 10 = 41 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 3d = 51 [SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE] 3d/3 = 51/3 d = [B]17[/B]

Nate jars 2 liters of jam everyday. How many days did Nate spend making jam if he jarred 8 liters of jam? 2 liters per 1 day and 8 liters per x days. Set up a proportion: 2/1 = 8/x Cross multiply: 2x = 8 Divide each side by 2 x = [B]4 days[/B].

[SIZE=5]Nervous Speaker #1 says the word "um" 8 times each minute. Nervous Speaker #2 says the word "um" 10 times each minute. Working together, how many minutes will it take them to say the word "um" 270 times? [/SIZE] [SIZE=4]In one minute, Nervous speaker 1 and 2 say "um" 8 + 10 = 18 times per minute. We want to know how many minutes it takes for both of them to say 270 "um"s. We divide 270/18 to get [B]15 minutes[/B][/SIZE]

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10? Let n be the number of notebooks you can purchase. We have the following inequality: 1.39n <= 10 Divide each side by 1.39 n <= 7.194 We want whole notebooks, we cannot buy fractions of notebooks, so we have: n <= 7 The question asks for the possible numbers of notebooks we can buy. This implies we buy at least 1, but our inequality says not more than 7. So our number set is: [B]N = {1, 2, 3, 4, 5, 6, 7}[/B]

N^2=5qd for d Divide each side by 5q to isolate d: N^2/5q = 5qd/5q Cancel 5q on the right side and we get: d = [B]N^2/5q[/B]

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip? Our percentage is found as 600/800. Simplifying by dividing top and bottom by 100, we have: 6/8 Divide top and bottom by 2, we get: 3/4 or [B]75% [/B] You can also type in the [URL='http://www.mathcelebrity.com/perc.php?num=600&den=800&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']search engine[/URL]: 600/800 as percent.

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000? 7% monthly is: 0.07/12 = .00583 So we have: 1000(1 + .00583)^m = 10000 divide each side by 1000; (1.00583)^m = 10 Take the natural log of both sides; LN (1.00583)^m = LN(10) Use the identity for natural logs and exponents: m * LN (1.00583) = 2.30258509299 0.00252458479m = 2.30258509299 m = 912.064867899 Round up to [B]913 months[/B]

Olivia bought 20 notebooks. Her cost for all of the notebooks was 2.00$. If each notebook cost the same amount then how much did she pay for one 20 notebooks / 2 Divide top and bottom by 20: 1 notebook = 2/20 1 notebook = 1/10 1 notebook = [B]10 cents[/B]

On a trip, a family drove 270 kilometers in 3 hours. how many kilometers were traveled in one hour. Express this as a rate per hour. 270 kilometers per 3 hours 270/3 Divide top and bottom by 3 to get km/hr [B]90 kilometers per hour[/B]

One fifth of the square of a number We have an algebraic expression. Let's break this into parts. [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The square of a number means we raise it to the power of 2. So we have x^2 [*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below: [/LIST] [B]x^2/5[/B]

One-fourth the sum of m and p Take this algebraic expression in parts: [LIST] [*]The sum of m and p means we add p to m: m + p [*]1/4 of the sum mean we divide m + p by 4 [/LIST] [B](m + p)/4[/B]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. One-half a number means we divide x by2: x/2 The word [I]is[/I] means equal to. We set x/2 equal to 50 for our algebraic expression [B]x/2 = 50 [/B] If the problem asks us to solve for x, we cross multiply: x = 2 * 50 x = [B]100[/B]

p = i^2r for r Divide each side of the equation by i^2 to isolate r: p/i^2 = i^2/ri^2 Cancel the i^2 on the right side and we get: r = [B]p/i^2[/B]

p is halved and 4 is added [U]p is halved means we divide p by 2:[/U] p/2 [U]4 is added:[/U] [B]p/2 + 4[/B]

P varies directly as q and the square of r and inversely as s There exists a constant k such that: p = kqr^2/s [I]Note: Direct variations multiply and inverse variations divide[/I]

p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6, what is the equation of variation? Two rules of variation: [LIST=1] [*]Varies directly means we multiply [*]Varies inversely means we divide [/LIST] There exists a constant k such that our initial equation of variation is: p = kr^2/qs [B][/B] With p = 40 when q = 5, r = 4 and s = 6, we have: 4^2k / 5 * 6 = 40 16k/30 = 40 Cross multiply: 16k = 40 * 30 16k = 1200 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=16k%3D1200&pl=Solve']equation calculator[/URL], we get: k = [B]75[/B] So our final equation of variation is: [B]p = 75r^2/qs[/B]

p/q=f/q-f for f To solve this literal equation for f, let's factor out f on the right side: p/q=f(1/q-1) Divide each side by (1/q - 1) p/(q(1/q - 1)) = f(1/q-1)/(1/q - 1) Cancelling the (1/q - 1) on the right side, we get: f = p/(1/q - 1) Rewriting this since (1/q -1) = (1 - q)/q since q/q = 1 we have: f = [B]pq/(1 - q)[/B]

P/v=nr/t for r Cross multiply to solve this literal equation: Pt = nrv Divide each side of the equation by nv: Pt/nv = nrv/nv Cancel the nv's on the right side, we get: r = [B]Pt/nv[/B]

p= 4/q what kind of variation is this? [B]Inverse Variation [/B]since we divide by q

Subtract 15 from each side: 5d/11 = P - 15 Multiply each side by 11 5d = 11p - 165 Divide each side of the equation by d: d = (11p - 165) ------------ 5

P=ab/c, for c Cross multiply: cP = ab Divide each side by P [B]c = (ab)/P[/B]

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Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width? The perimeter P of a rectangle with length l and width w is: 2l + 2w = P We're given P = 372 and l = 99, so we have: 2(99) + 2w = 372 2w + 198 = 372 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 198 and 372. To do that, we subtract 198 from both sides 2w + 198 - 198 = 372 - 198 [SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE] 2w = 174 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 174/2 w = [B]87[/B]

Pet supplies makes a profit of $5.50 per bag, if the store wants to make a profit of no less than $5225, how many bags does it need to sell? 5.5ob >= $5,225 Divide each side of the inequality by $5.50 b >=9.5 bags, so round up to a whole number of 10 bags.

Phyllis's mother has 6 pounds of candy to divide evenly among her 8 children. This is an average of how many pounds per child? 6 pounds divide among 8 children can be represented as a fraction. We want to simplify this. So we use our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F8&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], and we get: 3 pounds per 4 children, or 0.75 pounds per child.

Distance = Rate x Time 6.4 meters = 4 meters/minute * t Divide each side by 4 [B]t = 1.6 minutes[/B]

Time 1, distance apart is 105 + 85 = 190 So every hour, the distance between them is 190 * t where t is the number of hours. Set up our distance function: D(t) = 190t We want D(t) = 494 190t = 494 Divide each side by 190 [B]t = 2.6 hours[/B]

Find what was used: Used Money = Prepaid original cost - Remaining Credit Used Money = 20 - 17.47 Used Money = 2.53 Using (m) as the number of minutes, we have the following cost equation: C(m) = 0.11m C(m) = 2.53, so we have: 0.11m = 2.53 Divide each side by 0.11 [B]m = 23[/B]

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there? Let s be the standard version downloads and h be the high quality downloads. We have two equations: [LIST=1] [*]h = 3s [*]2.7s + 4.7h = 4200 [/LIST] Substitute (1) into (2) 2.7s + 4.7(3s) = 4200 2.7s + 14.1s = 4200 Combine like terms: 16.8s = 4200 Divide each side by 16.8 [B]s = 250[/B]

Pound of strawberries for $4.00. What is the price, in dollars, per ounce of strawberries? 1 pound equals 16 ounces. So the pounds per ounce equals: $4.00/16 ounces Divide top and bottom by 16, we get: [B]$0.25 per ounce[/B]

pr=xf/y for r So for this literal equation, we divide each side of the equation by p to isolate r. pr/p = xf/yp Cancel the p's on the left side and we get: r = [B]xf/yp [MEDIA=youtube]6ekuN4H3mM4[/MEDIA][/B]

Free Pressure Law Calculator - This will solve for any of the 4 items in the Pressure Law equation, also known as Gay-Lussacs Law assuming constant volume
P1 ÷ T1 = P2 ÷ T2

Prove the following statement for non-zero integers a, b, c, If a divides b and b divides c, then a divides c. If an integer a divides an integer b, then we have: b = ax for some non-zero integer x If an integer b divides an integer c, then we have: c = by for some non-zero integer y Since b = ax, we substitute this into c = by for b: c = axy We can write this as: c = a(xy) [LIST] [*]Since x and y are integers, then xy is also an integer. [*]Therefore, c is the product of some integer multiplied by a [*]This means a divides c [/LIST] [MEDIA=youtube]VUIUFAFFVU4[/MEDIA]

Let us take an integer x which is both even [I]and[/I] odd. [LIST] [*]As an even integer, we write x in the form 2m for some integer m [*]As an odd integer, we write x in the form 2n + 1 for some integer n [/LIST] Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1 Subtract 2n from each side: 2m - 2n = 1 Factor out a 2 on the left side: 2(m - n) = 1 By definition of divisibility, this means that 2 divides 1. But we know that the only two numbers which divide 1 are 1 and -1. Therefore, our original assumption that x was both even and odd must be false. [MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

pv/t = ab/c for c Cross multiply: cpv = abt Divide each side of the equation by pv to isolate c: cpv/pv = abt/pv Cancel the pv terms on the left side and we get: c = [B]abt/pv[/B]

quotient of the sum of 17 and x and y The sum of 17 and x means we add x to 17: 17 + x quotient of the sum of 17 and x and y means we divide 17 + x by y [B](17 + x)/y[/B]

r varies directly with s and inversely with the square root of t Varies directly means we multiply Varies inversely means we divide There exists a constant k such that: [B]r = ks/sqrt(t)[/B]

r=l^2w/2 for w Solve this literal equation by isolating w. Cross multiply: 2r = l^2w Divide each side by l^2 w = [B]2r/l^2[/B]

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's total purchase is $62. What equation can be used to find n, the number of scarves that Rebecca buys Scarves Cost + Purses Cost = Total Cost [U]Calculate Scarves Cost[/U] Scarves cost = Cost per scarf * number of scarves Scarves cost = 10n [U]Calculate Purses Cost[/U] Purses cost = Cost per purse * number of purses Purses cost = 16 * 2 Purses cost = 32 Total Cost = 62. Plug in our numbers and values to the Total Cost equation : 10n + 32 = 62 Solve for [I]n[/I] in the equation 10n + 32 = 62 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 32 and 62. To do that, we subtract 32 from both sides 10n + 32 - 32 = 62 - 32 [SIZE=5][B]Step 2: Cancel 32 on the left side:[/B][/SIZE] 10n = 30 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 30/10 n = [B]3[/B]

raise 2 to the 10th power and divide k by the result Raise 2 to the 10th power: 2^10 Divide k by the result: k / 2^10

raise 3 to the 4th power, subtract w from the result, then divide v by what you have Raise 3 to the 4th power: 3^4 Simplified, this is 81 Subtract w from the result. We subtract w from 81: 81 - w Then divide v by what you have. We divide v by (81 -w) [B]v/(81 - w)[/B]

raise 3 to the 8th power, then divide the result by t 3 to the 8th power 3^8 Divide the result by t 3^8/t Now, if they want you to evaluate 3 to the 8th, you have: 6,561/t

Raise 9 to the 3rd power, subtract d from the result, then divide what you have by c. This is an algebraic expression, let's take in parts (or chunks). Raise 9 to the 3rd power. This means we take 9, and raise it to an exponent of 3 9^3 Subtract d from the result, means we subtract d from 9^3 9^3 - d Now we divide 9^3 - d by c [B](9^3 - d) / c[/B]

Raise c to the 7th power, divide the result by 4, then triple what you have. Take this algebraic expression in pieces. Raise c to the 7th power: c^7 Divide the result by 4, means we divide c^7 by 4 c^7 / 4 Triple what you have means multiply c^7 / 4 by 3 [B]3(c^7 / 4)[/B]

raise f to the 3rd power, then find the quotient of the result and g Take this algebraic expression in two parts: [LIST=1] [*]Raise f to the 3rd power means we take f, and write it with an exponent of 3: f^3 [*]Find the quotient of the result and g. We take f^3, and divide it by g [/LIST] [B]f^3/g[/B]

Raise f to the 8th power, divide the result by 5, then multiply 10 f to the 8th power means we raise f to the power of 8 using an exponent: f^8 Divide f^8 by 5 (f^8)/5 Now multiply this by 10: 10(f^8)/5 We can simplify this algebraic expression by dividing 10/5 to get 2 on top: 2[B](f^8)[/B]

Raise F to the second power then divide G by the result F to the second power: F^2 Divide G by the result: [B]G/F^2[/B]

Raise p to the 9th power, multiply the result by q, then divide what you have by r. Take this in steps: [LIST] [*]Raise p to the 9th power: p^9 [*]Multiply the result by q: qp^9 [*]Divide what you have (the result) by r: qp^9/r [/LIST] [B](qp^9)/r [MEDIA=youtube]I5PShTfas4Y[/MEDIA][/B]

raise q to the 5th power add the result to p then divide what you have by r Take this algebraic expression in parts: [LIST] [*]Raise q to the 5th power: q^5 [*]Add the result to p: p + q^5 [*]Divide what you have by r. This means we take our result above and divide it by r: [/LIST] [B](p + q^5)/r[/B]

V to the 9th power means we use an exponent: v^9 Divide that result by u [B]v^9/u[/B]

raise x to the 10th power, then divide b by the result x to the 10th power x^10 Divide b by the result: [B]b/x^10[/B]

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ratio of the squares of t and u Ratio is also known as quotient in algebraic expression problems. The square of t means we raise t to the power of 2: t^2 The square of u means we raise u to the power of 2: u^2 ratio of the squares of t and u means we divide t^2 by u^2: [B]t^2/u^2[/B]

Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below 3x + 2y 1 -------- = --- 4x + y 3 [LIST] [*]x = 7y/13 [*]x = 7y/5 [*]x = -7y [*]x = -3y [*]x = 3y/5 [*]x = -5y/13 [*]x = -y [/LIST] Cross multiply: 3(3x - 2y) = 4x + y Multiply the left side through 9x - 6y = 4x + y Subtract 4x from each side and add 6y to each side 5x = 7y Divide each side by 5 to isolate x, the subject of an equation is the variable to the left [B]x = 7y/5[/B]

Free Relative Error Calculator - Relative error is the absolute error divided by quantity

Let x be the price of one t-shirt. Set up an equation: 6 times the number of t-shirts plus 7 dollars left over get him to a total of 45 6x = 45 - 7 6x = 38 Divide each side by 6 [B]x = 6.33[/B]

Ronald scored 4 goals in his first soccer game. He then scored the same amount of goals in his next 3 games. If Ronald has 10 goals total, how many did he score in each game? For the remaining 3 games, he scored 10 - 4 = 6 goals. 6 goals divided by 3 games = [B]2 goals in each game[/B].

Roster form of: A = {3x-2/x are integers between 0 and 8} x = 0 = Undefined since we divide by 0 x = 1: 3*1 + 2/1 = 5 x = 2: 3*2 + 2/2 = 7 x = 3: 3*3 + 2/3 = 9.66666666666667 x = 4: 3*4 + 2/4 = 12.5 x = 5: 3*5 + 2/5 = 15.4 x = 6: 3*6 + 2/6 = 18.3333333333333 x = 7: 3*7 + 2/7 = 21.2857142857143 x = 8: 3*8 + 2/8 = 24.25 [B]A = {(0, undefined), (1, 5), (2, 7), (3, 9.6667), (4, 12.5), (5, 15.4), (6, 18.3333), (7, 21.2857142857143), (8, 24.25)}[/B]

s = tu^2 for u Divide each side by t u^2 = s/t Take the square root of each side [LIST] [*]u = sqrt(s/t) [*]u = -sqrt(s/t) [/LIST] We have two answers due to negative number squared is positive

s=u^2t for t Divide each side by u^2 to isolate t: u^2t/u^2 = s/u^2 Cancel the u^2 on the left side, we get: t = [B]s/u^2[/B]

Salma purchased a prepaid phone card for 30. Long distance calls cost 9 cents a minute using this card. Salma used her card only once to make a long distance call. If the remaining credit on her card is 28.38, how many minutes did her call last? [U]Set up the equation where m is the number of minutes used:[/U] 0.09m = 30 - 28.38 0.09m = 1.62 [U]Divide each side by 0.09[/U] [B]m = 18[/B]

Sarah has 12 apples she divided them in 4 groups. How many are in each group? 12 apples per group divided by 4 groups is written as: 12/4 So we have [B]3 groups[/B].

Scientists are studying a cell that divides in half every 15 minutes. How many cells will there by after 2.5 hours? Divide 2.5 hours into 15 minute blocks. 2.5 hours = 2(60) + 0.5(60) minutes 2.5 hours = 120 + 30 minutes 2.5 hours = 150 minutes Now determine the amount of 15 minute blocks 150 minutes/15 minutes = 10 blocks or divisions [LIST] [*]We start with 1 cell at time 0, and double it every 15 minutes [*]We have A(0) = 1, we want A(10). [*]Our accumulation function is A(t) = A(0) * 2^t [/LIST] A(10) = 1 * 2^10 A(10) = [B]1024[/B]

Scott and Dylan both leave the park at the same time, but in opposite directions. If Scott travels 12 mph and Dylan travels 19 mph, how long until they are 186 miles apart? Hour 1, they are 19 + 12 = 31 miles apart. So each hour, they get 31 miles more apart. When they are [URL='https://www.mathcelebrity.com/fraction.php?frac1=186%2F31&frac2=3%2F8&pl=Simplify']186 miles apart[/URL], we divide this by 31 miles apart per hour: 186/31 = [B]6 hours[/B]

[U]Two digit Numbers less than 56:[/U] {10, 11, 12, ..., 55} [U]Two Digit Even Numbers of that Set:[/U] {10, 12, 14, ..., 54} [U]Two Digit Even numbers Divisible by 5[/U] [B]C = {10, 20, 30, 40, 50}[/B] [I]Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is even numbers only, end in 0. [MEDIA=youtube]aQKLVxIB-p4[/MEDIA][/I]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first? Let p be the number of plums Shalini started with. We have: [LIST] [*]0.4 given to her brother [*]20% which is 0.2 given away to her sister [*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself [/LIST] 0.4p = 16 Divide each side by 0.4 [B]p = 40[/B]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How many plums did she have first? Let's convert everything to decimals. 20% = 0.2 So Shalini gave 0.4 + 0.2 = 0.6 of the plums away. Which means she has 1 = 0.6 = 0.4 or 40% left over. 40% represents 16 plums So our equation is 0.4p = 16 where p is the number of plums to start with Divide each side by 0.4 [B]p = 40[/B]

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza? [U]Determine additional amount the pizzas would have cost without the coupon[/U] 6 pizzas * 3 per pizza = 18 [U]Add 18 to our discount price of 38.94[/U] Full price for 6 large pizzas = 38.94 + 18 Full price for 6 large pizzas = 56.94 Let x = full price per pizza before the discount. Set up our equation: 6x = 56.94 Divide each side by 6 [B]x = $9.49[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be? Sheila wants: [LIST=1] [*]l =5w [*]2l + 2w = 100 <-- Perimeter [/LIST] Substitute (1) into (2) 2(5w) + 2w = 100 10w + 2w = 100 12w = 100 Divide each side by 12 [B]w = 8.3333[/B] Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Since pounds are smaller than tons, i need to ______ the number of pounds by _____ [B]Divide[/B] the number of pounds by [B]2,000[/B]

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v 1/2(2/5) = 1/5 since the 2's cancel r^2/r^2 = 1 So we simplify, and get: mgh=1/2mv^2+1/5(mv^2) for v Divide each side by m, so m's cancel in each term on the left and right side: gh = 1/2v^2 + 1/5(v^2) Combine like terms for v^2 on the right side: 1/2 + 1/5 = 7/10 from our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction calculator[/URL] So we have: gh = 7v^2/10 Multiply each side by 10: 10gh = 7v^2 Now divide each side by 7 10gh/7 = v^2 Take the square root of each side: [B]v = sqrt(10gh/7)[/B]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about? Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet. [LIST] [*]Rangers's height = n [*]Tree height = 64n [*]Smaller tree height = 64n - 112 [*]Total height = 64n - 112 + 64n = 597.5 [/LIST] Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (64 + 64)n = 128n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 128n - 112 = + 597.5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -112 and 597.5. To do that, we add 112 to both sides 128n - 112 + 112 = 597.5 + 112 [SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE] 128n = 709.5 [SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE] 128n/128 = 709.5/128 n = 5.54296875 Tree height = 64 * ranger height Tree height = 64 * 5.54296875 Tree height = [B]354.75 feet[/B]

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second. i. After how many seconds will Sophie catch Claire? ii. If the race is 500 feet, who wins? i. Sophie's distance formula is given as D = 5s Claire's distance formula is given as D = 3s + 100 Set them equal to each other 5s = 3s + 100 Subtract 3s from both sides: 2s = 100 Divide each side by 2 [B]s = 50[/B] ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Square root of 9136 divided by 43 First, [URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%289136%29&pl=Calculate']take the square root of 9136 in our calculator[/URL]: 4 * sqrt(571) Now divide this by 43: [B]4 * sqrt(571) / 43[/B]

Standard Error (margin of Error) = Standard Deviation / sqrt(n) 128 = 545/sqrt(n) Cross multiply: 128sqrt(n) = 545 Divide by 128 sqrt(n) = 4.2578125 Square both sides: [B]n = 18.1289672852 But we need an integer, so the answer is 19[/B]

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick? Let r be the cost of the ruler Let y be the cost of the yardstick We're given 2 equations: [LIST=1] [*]r + y = 1.25 [*]y = r + 0.45 [/LIST] Substitute equation (2) into equation (1) for y r + r + 0.45 = 1.25 Solve for [I]r[/I] in the equation r + r + 0.45 = 1.25 [SIZE=5][B]Step 1: Group the r terms on the left hand side:[/B][/SIZE] (1 + 1)r = 2r [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2r + 0.45 = + 1.25 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.45 and 1.25. To do that, we subtract 0.45 from both sides 2r + 0.45 - 0.45 = 1.25 - 0.45 [SIZE=5][B]Step 4: Cancel 0.45 on the left side:[/B][/SIZE] 2r = 0.8 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2r/2 = 0.8/2 r = 0.4 Substitute r = 0.4 into equation (2) above: y = r + 0.45 y = 0.4 + 0.45 r = [B]0.85 [URL='https://www.mathcelebrity.com/1unk.php?num=r%2Br%2B0.45%3D1.25&pl=Solve']Source[/URL][/B]

Start with q. Multiply by p. Add 3. Divide A Start with q: q Multiply by p: pq Add 3: pq + 3 Divide A means divide by A. We wrap pq + 3 in parentheses to divide by the sum (pq + 3)/A

Start with t , add 6, divide by 2, then subtract 5. Start with t: t Add 6: t + 6 Divide by 2: (t + 6)/2 [I]Add parentheses because we're dividing the [U]quantity[/U] by 2 [/I] Then subtract 5: [B](t + 6)/2 - 5[/B]

Stephanie spent $6.95 on these 12 chocolates. What was the cost of each chocolate? Give your answer to the nearest 5 cents $6.95/12 chocolates Divide top and bottom by 12 to get the cost per one chocolate: $6.95/12 = 0.58 cents per chocolate The problem asks us to round to the nearest [I]5 cents[/I]. 5 * 11 = 55 5 * 12 = 60 Since 58 cents is closer to 60, we have [B]60 cents[/B] as our answer

subtract half of a number from 10 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x half of a number means we divide x by 2: x/2 subtract half of a number from 10 [B]10 - x/2[/B]

Subtract the quotient of m and 7 from 4 The quotient of m and 7 means we add divide m by 7 m/7 Subtract this quotient from 4 [B]4 - m/7[/B]

sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4 2) We increment by 2 for each number since we have [I]odd numbers[/I]. 3) We set this sum of consecutive [I]odd numbers[/I] equal to 117 n + (n + 2) + (n + 4) = 117 [SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE] (n + n + n) + 2 + 4 = 117 3n + 6 = 117 [SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE] 3n + 6 - 6 = 117 - 6 [SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE] 3n + [S]6[/S] - [S]6[/S] = 117 - 6 3n = 111 [SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE] 3n/3 = 111/3 [SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE] [S]3[/S]n/[S]3 [/S]= 111/3 n = 37 Call this n1, so we find our other 2 numbers n2 = n1 + 2 n2 = 37 + 2 n2 = 39 n3 = n2 + 2 n3 = 39 + 2 n3 = 41 [SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE] ([B]37, 39, 41[/B]) 37 ? 1st number, or the Smallest, Minimum, Least Value 39 ? 2nd number 41 ? 3rd or the Largest, Maximum, Highest Value

sum of the cube of x and half of y The cube of x means we raise x to the 3rd power: x^3 half of y means we divide y by 2: y/2 sum of the cube of x and half of y means we add y/2 to x^3 [B]x^3 + y/2[/B]

sum of x plus y divided by 2 sum of x plus y: x + y sum of x plus y divided by 2 [B](x + y)/2[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have? Set up two equations where d is the number of dimes and q is the number of quarters: (1) d + q = 10 (2) 0.1d + 0.25q = 1.45 Rearrange (1) into (3) to solve for d (3) d = 10 - q Now plug (3) into (2) 0.1(10 - q) + 0.25q = 1.45 Multiply through: 1 - 0.1q + 0.25q = 1.45 Combine q terms 0.15q + 1 = 1.45 Subtract 1 from each side 0.15q = 0.45 Divide each side by 0.15 [B]q = 3[/B] Plug our q = 3 value into (3) d = 10 - 3 [B]d = 7[/B]

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x. [U]Use the quotient remainder theorem[/U] A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B Plugging in our numbers for Equation 1 we have: [LIST] [*]A = x [*]B = 7 [*]Q = q [*]R = 6 [*]x = 7 * q + 6 [/LIST] Plugging in our numbers for Equation 2 we have: [LIST] [*]A = x [*]B = 11 [*]Q = q [*]R = 2 [*]x = 11 * q + 2 [/LIST] Set both x values equal to each other: 7q + 6 = 11q + 2 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get: q = 1 Plug q = 1 into the first quotient remainder theorem equation, and we get: x = 7(1) + 6 x = 7 + 6 [B]x = 13[/B] Plug q = 1 into the second quotient remainder theorem equation, and we get: x = 11(1) + 2 x = 11 + 2 [B]x = 13[/B]

T = mg - mf for f Subtract mg from each side: T - mg = mg - mg - mf Cancel the mg on the right side and we get: T - mg = -mf Multiply each side by -1: -(T - mg) = -(-mf) mg - T = mf Now Divide each side by m to isolate f: (mg - T)/m = mf/m Cancel the m on the right side and we get: f = [B](mg - T)/m[/B]

t varies directly with the square of r and inversely with w There exists a constant k such that: [B]t = kr^2/w[/B] [I]Directly means multiply and inversely means divide[/I]

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total We have a commission equation below: Sales * Commission percent = Salary We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have: Sales * 0.04 = 55,000 Divide each side of the equation by 0.04, and we get: Sales = [B]1,375,000[/B]

Taylor is playing a game using a die and a spinner. The spinner is divided into 4 equal parts with colors green, red, yellow, and purple. Taylor rolls the die and spins the spinner. What is the probability the die shows a 2 and the spinner lands on purple? Probability of rolling a 2 on the die is 1/6 Probability of getting a purple on the spinner is 1/4 Since each event is independent, our joint probability is: P(2 on the die and Purple on the spinner) = P(2 on the die) x P(Purple on the Spinner) P(2 on the die and Purple on the spinner) = 1/6 x 1/4 P(2 on the die and Purple on the spinner) = [B]1/24[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother? [LIST] [*]Let the height of the family without the mom be f. Let the height of the mother be m. [*]Averages mean we add the heights and divide by the number of people who were measured. [/LIST] We're given two equations: [LIST=1] [*](f + m)/6 = 6 [*]f/5 = 6 [/LIST] Cross multiplying equation (2), we get: f = 5 * 6 f = 30 Plug f = 30 into equation (1), we get: (30 + m)/6 = 6 Cross multiplying, we get: m + 30 = 6 * 6 m + 30 = 36 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get: m = [B]6[/B] [SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x. The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have: (16 + x)/2 = 21 Cross multiply: 16 + x = 21*2 16 + x = 42 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B]. Check our work by restating our answer: The average of 16 and 26 is 21. TRUE.

The average of 171 and x? The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set. Our number set in this case is {171, x} which has 2 elements. Therefore, our average is: [B](171 + x)/2[/B]

Let x equal "a number". Double the number is 2x. The average is (x + 2x)/2 Combine the terms in the numerator: 3x/2 The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5 3x/2 = 25.5 Cross multiply the 2: 3x = 51 Divide each side by 3 [B]x = 17[/B]

the average of eighty-five and a number m is ninety Average of 2 numbers means we add both numbers and divide by 2: (85 + m)/2 = 90 Cross multiply: m + 85 = 90 * 2 m + 85 = 180 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get: m = [B]95[/B]

the average of two numbers x and y Average is the sum divided by the count: Sum: x + y We have 2 numbers, so we divide (x + y) by 2 [B](x + y)/2[/B]

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle We're given: b=2/7A We're also told that b is less than 10. So we have: 2/7A < 10 2A/7 < 10 Cross multiply: 2A < 7 * 10 2A < 70 Divide each side of the inequality by 2 to isolate A 2A/2 < 70/2 Cancel the 2's on the left side and we get: A < [B]35[/B]

The club uses the function S(t) = -4,500t + 54,000 to determine the salvage S(t) of a fertilizer blender t years after its purchase. How long will it take the blender to depreciate completely? Complete depreciation means the salvage value is 0. So S(t) = 0. We need to find t to make S(t) = 0 -4,500t + 54,000 = 0 Subtract 54,000 from each side -4,500t = -54,000 Divide each side by -4,500 [B]t = 12[/B]

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95? Setup the inequality: $19.50 + $7.95x < $95 Subtract 19.50 from both sides: 7.95x < 75.50 Divide each side of the inequality by 7.95 to isolate x x < 9.5 The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B]. Check our work: $7.95 * 9.5 + $19.50 $71.55 + $19.50 = $91.05

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y Take this in algebraic expression in parts: [U]Term 1[/U] [LIST] [*]The square of y means we raise y to the 2nd power: y^2 [*]5 times the square of y: 5y^2 [/LIST] [U]Term 2[/U] [LIST] [*]2 times y: 2y [*]The square of 2 times y: (2y)^2 = 4y^2 [*]7 divide by the square of 2 times y: 7/4y^2 [/LIST] [U]The difference of these terms is written as Term 1 minus Term 2:[/U] [LIST] [*]5y^2/4y^2 [/LIST] [U]The cube of the difference means we raise the difference to the power of 3:[/U] [B](5y^2/4y^2)^3[/B]

The difference between the quotient of x and y, and twice z The quotient of x and y means we divide x by y: x/y Twice z means we multiply z by 2: 2z The difference between the quotient of x and y, and twice z means we subtract 2z from x/y [B]x/y - 2z[/B]

The difference between the squares of two consecutive numbers is 141. Find the numbers Take two consecutive numbers: n- 1 and n Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is: 2n - 1 = d Proof of this: n^2- (n - 1)^2 = d n^2 - (n^2 - 2n + 1) = d n^2 - n^2 + 2n - 1 = d 2n - 1 = d Given d = 141, we have 2n - 1 = 141 Add 1 to each side: 2n = 142 Divide each side by 2: 2n/2 = 142/2 n = [B]71[/B] Therefore, n - 1 = [B]70 Our two consecutive numbers are (70, 71)[/B] Check your work 70^2 = 4900 71^2 = 5041 Difference = 5041 - 4900 Difference = 141 [MEDIA=youtube]vZJtZyYWIFQ[/MEDIA]

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers. Let the numbers be x and y. We have: [LIST] [*]x - y = 54 [*]x/y = 4 [*]Cross multiply x/y = 4 to get x = 4y [*]Now substitute x = 4y into the first equation [*](4y) - y = 54 [*]3y = 54 [*]Divide each side by 3 [*][B]y = 18[/B] [*]If x = 4y, then x = 4(18) [*][B]x = 72[/B] [/LIST]

the difference of 4 and the quotient of 18 and a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The quotient of 18 and a number means we divide 18 by the variable x. 18/x The difference of 4 and the quotient above means we subtract 18/x from 4: [B]4 - 18/x[/B]

The difference of five and five y 5 - 5y eight and two y 8 + 2y The phrase [I]is the same as[/I] means equal to. Set 5 - 5y equal to 8 + 2y for our final algebraic expression [B]5 - 5y = 8 + 2y[/B] [B][/B] If the problem asks you to solve for y: Add 5y to each side: 5 = 8 + 7y Subtract 8 from each side: 7y = -3 Divide each side by 7: [B]y= -3/7[/B]

The doctor told Anna that tomorrow she will have to check her blood pressure every 15 minutes from 10:00 AM to 4:00 PM. How many times does she have to take her blood pressure? 10:00 A.M. to 4:00 P.M. is 6 hours. Each hour is 60 minutes 60 minutes divided by 15 minutes equals 4 blood pressure checks per hour. 4 blood pressure checks per hour * 6 hours = [B]24 blood pressure checks[/B]

The enrollment at a gymnastics academy increased 120% from 2016 to 2017. The enrollment in 2017 was 210. What is 2016's enrollment? We take 2017's enrollment of 210 and divide by 1.2 since 120% is 1.2 as a multiplier: 2016 enrollment = 2017 enrollment / 1.2 2016 enrollment =210/1.2 2016 enrollment = [B]175[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Digit, Probability 1, 0.301 2, 0.176 3, 0.125 4, 0.097 5, 0.079 6, 0.067 7, 0.058 8, 0.051 9, 0.046 [B][U]Fradulent Checks[/U][/B] Digit, Frequency 1, 36 2, 32 3, 45 4, 20 5, 24 6, 36 7, 15 8, 16 9, 7 Complete parts (a) and (b). (a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?
Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction? We're given two equations with a fraction with numerator (n) and denominator (d): [LIST=1] [*]n + d = 40 [*]n/d = 3/5 [/LIST] Cross multiply equation 2, we get: 5n = 3d Divide each side by 5: 5n/5 = 3d/5 n = 3d/5 Substitute this into equation 1: 3d/5 + d = 40 Multiply through both sides of the equation by 5: 5(3d/5) = 5d = 40 * 5 3d + 5d =200 To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%2B5d%3D200&pl=Solve']type it in our search engine and we get[/URL]: d = [B]25 [/B] Now substitute that back into equation 1: n + 25 = 40 Using [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B25%3D40&pl=Solve']our equation solver again[/URL], we get: n = [B]15[/B]

The function f(x) = x^3 - 48x has a local minimum at x = and a local maximum at x = ? f'(x) = 3x^2 - 48 Set this equal to 0: 3x^2 - 48 = 0 Add 48 to each side: 3x^2 = 48 Divide each side by 3: x^2 = 16 Therefore, x = -4, 4 Test f(4) f(4) = 4^3 - 48(4) f(4) = 64 - 192 f(4) = [B]-128 <-- Local minimum[/B] Test f(-4) f(-4) = -4^3 - 48(-4) f(-4) = -64 + 192 f(-4) = [B]128 <-- Local maximum[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time. Average Velocity: [ f(3) - f(0) ] / ( 3 - 0 ) Calculate f(3): f(3) = -4.9(3^2) + 300 f(3) = -4.9(9) + 300 f(3) = -44.1 + 300 f(3) = 255.9 Calculate f(0): f(0) = -4.9(0^2) + 300 f(0) = 0 + 300 f(0) = 300 So we have average velocity: Average velocity = (255.9 - 300)/(3 - 0) Average velocity = -44.1/3 Average velocity = -[B]14.7 [/B] Velocity is the first derivative of position s(t)=-4.9t^2 +300 s'(t) = -9.8t So we set velocity equal to average velocity: -9.8t = -14.7 Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What is the probability that a randomly person has an IQ between 85 and 115? b) Find the 90th percentile of the IQ distribution c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean? a) [B]68%[/B] from the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL] b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)
(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: [LIST=1] [*]l = 3w [*]P = 80 = 2l + 2w = 80 [/LIST] Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = [B]10 [/B] Substitute w = 10 into (1) l = 3(10) l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. P = 2l + 2w Since P = 120, we have: (1) 2l + 2w = 120 We are also given: (2) l = 3w - 6 Substitute equation (2) into equation (1) 2(3w - 6) + 2w = 120 Multiply through: 6w - 12 + 2w = 120 Combine like terms: 8w - 12 = 120 Add 12 to each side: 8w = 132 Divide each side by 8 to isolate w: w =16.5 Now substitute w into equation (2) l = 3(16.5) - 6 l = 49.5 - 6 l = 43.5 So (l, w) = (43.5, 16.5)

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width? 5.8 feet less than 6 times the width is an algebraic expression: 6w - 5.8 We set this equal to the length of 50.6 6w - 5.8 = 50.6 Add 5.8 to each side: 6w - 5.8 + 5.8 = 50.6 + 5.8 Cancel the 5.8 on the left side: 6w = 56.4 Divide each side by 6: 6w/6 = 56.4/6 [URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B]. [MEDIA=youtube]gfM-d_Ej728[/MEDIA]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width. A flag is a rectangle shape. So we have the following equations Since P = 2l + 2w, we have 2l + 2w = 60 l = 7w - 2 Substitute Equation 1 into Equation 2: 2(7w -2) + 2w = 60 14w - 4 + 2w = 60 16w - 4 = 60 Add 4 to each side 16w = 64 Divide each side by 16 to isolate w w = 4 Which means l = 7(4) - 2 = 28 - 2 = 26

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number? The mean of 3 numbers is the sum of 3 numbers divided by 3. Let the 3rd number be n. We have: Mean = (21 + 35 + n) / 3 The Mean is given as 20, so we have: 20 = (n + 56) / 3 Cross multiply: n + 56 = 20 * 3 n + 56 = 60 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B56%3D60&pl=Solve']type this number in our search engine [/URL]and we get: n = [B]4[/B]

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to rent? Rent Payment Fraction = Rent Payment / Total Income Rent Payment Fraction = 1600 / 3840 Our greatest common factor of 1600 and 3840 is 320. So if we divide 1600 and 3840 by 320, we get: Rent Payment Fraction = [B]5/12 [MEDIA=youtube]DsXk6AKT18M[/MEDIA][/B]

We want to see votes per dollar. So we divide 50 million votes by $5 million dollars. 50,000,0000 ------------ 5,000,000 We have 10 votes for every dollar spent. Or, ten cents per vote.

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle. l = 4w - 15 Perimeter = 2l + 2w Substitute, we get: 400 = 2(4w - 15) + 2w 400 = 8w - 30 + 2w 10w - 30 = 400 Add 30 to each side 10w = 370 Divide each side by 10 to isolate w w = 37 Plug that back into our original equation to find l l = 4(37) - 15 l = 148 - 15 l = 133 So we have (l, w) = (37, 133)

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal? Minutes Rachel talks = m Current plan cost = 0.12m New plan cost = 0.005m + 46 Set new plan equal to current plan: 0.005m + 46 = 0.12m Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides 0.005m + 46 - 0.12m = 0.12m - 0.12m [SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE] -0.115m + 46 = 0 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 46 and 0. To do that, we subtract 46 from both sides -0.115m + 46 - 46 = 0 - 46 [SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE] -0.115m = -46 [SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE] -0.115m/-0.115 = -46/-0.115 m = [B]400 She must talk over 400 minutes for the new plan to be a better deal [URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack? backpack cost = b Cheap backpack = b - 15 The total of both items equals 75: b + b - 15 = 75 Solve for [I]b[/I] in the equation b + b - 15 = 75 [SIZE=5][B]Step 1: Group the b terms on the left hand side:[/B][/SIZE] (1 + 1)b = 2b [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2b - 15 = + 75 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -15 and 75. To do that, we add 15 to both sides 2b - 15 + 15 = 75 + 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] 2b = 90 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2b/2 = 90/2 b = 45 Cheap backpack = 45 - 15 = [B]30 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb-15%3D75&pl=Solve']Source[/URL][/B]

the product of a number and 15 is not less than 15 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x the product of a number and 15 means we multiply x by 15 15x The phrase [I]not less than[/I] means greater than or equal to. We set 15x greater than prequel to 15 [B]15x >= 15 <-- This is our algebraic expression [/B] [U]If the problem asks you to solve for x:[/U] Divide each side by 15: 15x/15 >= 15/15 [B]x >= 1[/B]

The quantity x minus y divided by 4 The quantity x minus y x - y The quantity x minus y divided by 4 [B](x - y)/4[/B]

The quotient of 2 and the sum of a number and 1. The phrase [I]a number[/I] represents an arbitrary variable, let's call it x. The sum of a number and 1 is written as: x + 1 The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1 2 -------- ( x + 1)

the quotient of 3 and u is equal to 52 divided by u Take this algebraic expression in 3 parts: [LIST=1] [*]The quotient of 3 and u means we divide 3 by u: 3/u [*]52 divided by u means we divide 52 by u: 52/u [*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2) [/LIST] [B]3/u = 52/u[/B]

the quotient of 4 more than a number and 7 is 10 Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 more than a number means we add 4 to x: x + 4 The quotient of 4 more than a number and 7 means we divide x + 4 by 7 (x + 4)/7 The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 [B](x + 4)/7 = 10[/B]

the quotient of a number and twice another number The phrase[I] a number [/I]means an arbitrary variable, let's call it x. The phrase[I] another number [/I]means another arbitrary variable, let's call it y. Twice means we multiply y by 2:2y The quotient means we divide x by 2y: [B]x/2y[/B]

the quotient of m and the sum of n and p. The sum of n and p means we add p to n: n + p The quotient means a fraction, so we divide m by (n + p) [B]m/(n + p)[/B]

the quotient of m squared and a squared [U]m squared means we raise m to the power of 2:[/U] m^2 [U]a squared means we raise a to the power of 2:[/U] a^2 [U]The [I]quotient[/I] means we divide m^2 by a^2:[/U] [B]m^2/a^2[/B]

the ratio of 50 and a number added to the quotient of a number and 10 Take this algebraic expression in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The ratio of 50 and x means we divide by 50 by x 50/x The quotient of a number and 10 means we have a fraction: x/10 The phrase [I]added to[/I] means we add 50/x to x/10 [B]50/x + x/10[/B]

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees? Let the smallest angle be x. Then we have 3 angles based on the ratio: x, 2x, 3x We know the sum of the angles of a triangle equals 180. So we have: x + 2x + 3x = 180 6x = 180 Divide each side by 6: 6x/6 = 180/6 x = 30 The largest angle is 3(30) = [B]90 [MEDIA=youtube]l8Lc6YtK9dg[/MEDIA][/B]

The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase? If Kyle bought the player, he has 243 - 210 = 33 left over. Each cd is 11, so set up an equation to see how many CDs he bought: 11x = 33 Divide each side by 11 [B]x = 3[/B]

The sales tax on a computer was $33.60. If the sales tax rate is 7%, how much did the computer cost without tax? Let the cost of the computer be c. We have: 0.07c = 33.60 Solve for [I]c[/I] in the equation 0.07c = 33.60 [SIZE=5][B]Step 1: Divide each side of the equation by 0.07[/B][/SIZE] 0.07c/0.07 = 33.60/0.07 c = $[B]480[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%3D33.60&pl=Solve']Source[/URL]

The scale of a map shows that 1/2 inch is equal to 3/4 of a mile. How many inches on a map would be equal to 3 miles? Set up a proportion of scale to actual distance 1/2 / 3/4 = x/3 4/3 = x/3 Cross multiply: 3x = 12 Divide each side by 3: 3x/3 = 12/3 x = [B]4 (1/2 inch sections) or 2 inches[/B]

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how many cars they have to wash to earn at least 300 Let x be the number of cars they wash. Set up our inequality. Note, at least 300 means 300 or greater, so we use greater than or equal to. [U]Inequality:[/U] [B]4.50x >= 300 [/B] [U]So solve for x, divide each side by 4[/U] [B]x >= 66.67[/B]

the set of natural numbers less than 7 that are divisible by 3 Natural Numbers less than 7 {1, 2, 3, 4, 5, 6} Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder: [B]{3, 6}[/B]

The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equations to determine the numbers. Let the two numbers be x and y. We have the following equations: [LIST=1] [*]x + y = 70 [*]x - y = 24 [/LIST] Add (1) to (2): 2x = 94 Divide each side by 2 [B]x = 47[/B] Plug this into (1) 47 + y = 70 Subtract 47 from each side, we have: [B]y = 23[/B]

the sum of 3 numbers divided by its product The phrase [I]3 numbers[/I] means we choose [I]3[/I] arbitrary variables. Let's call them x, y, z. The sum of of these 3 numbers is: x + y + z The phrase [I]its product[/I] means we multiply all 3 arbitrary variables together: xyz Now, the phrase [I]divided by[/I] means we divide x + y + z by xyz: [B](x + y + z)/xyz[/B]

The sum of 3h and k divided by 2 The sum of 3h and k 3h + k Divided by 2: [B](3h + k)/2[/B]

the sum of 4 and x split into 5 equal parts The sum of x and 4 means we add 4 to x: x + 4 Whenever you see the phrase [I]split into[/I], think of divide or divided by: [B](x + 4)/5[/B]

The sum of 80 and 40 is divided by 5 The sum of 80 and 40: 80 + 40 Divided by 5: [B](80 + 40)/5[/B]

The sum of a and b divided by their product The sum of a and b means we add b to a: a + b The product of a and b means we multiply a by b: ab To get our final algebraic expression, we divide the sum (a + b) by the product ab: [B](a + b)/ab[/B]

the sum of a and b, divided by the product of c and d The sum of a and b, means we add b to a a + b The product of c and d means we multiply c by d cd Divided by means we divide a + b by cd [B](a + b)/cd[/B]

The sum of a number and 5 all divided by 2 is 17 The phrase [I]a number[/I] means an arbitrary variable, let's call it x x The sum of a number and 5: x + 5 All divided by 2: (x + 5)/2 The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17: [B](x + 5)/2 = 17[/B]

The sum of a number and 5 divided by 8. Let's take this algebraic expression in parts. Part 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Part 2: The sum of a number and 5 means we add 5 to the number x x + 5 Part 3: Next, we divide this expression by 8 [B](x + 5)/8[/B]

A number means an arbitrary variable, let's call it x. The sum of a number and itself means adding the number to itself x + x Simplified, we have 2x The word is means equal to, so we have an algebraic expression of: [B]2x= 8 [/B] IF you need to solve this equation, divide each side by 2 [B]x = 4[/B]

"A Number" means an arbitrary variable, let's call it x. x divide d by 8 is written as a quotient x/8 The sum of x/8 and 3 means we add: x/8 + 3 Finally, equals means we have an equation, so we set our expression above equal to 6 x/8 + 3 = 6

The sum of m and 3 divided by the difference of m minus 3. Sum of m and 3: m + 3 Difference of m minus 3 m - 3 Take a quotient of these expressions: [B]m + 3 ------- m - 3[/B]

Twice n means we multiply n by 2 2n The sum of n and twice n means we add n + 2n The word [I]is[/I] means equal to, so we set that expression above equal to 12 n + 2n = 12 Combine like terms: 3n = 12 Divide each side of the equation by 3 to isolate n n = 4 Check our work Twice n is 2*4 = 8 Add that to n = 4 8 + 4 12

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number? Let x and (16-x) represent the original ten and units digits respectively Reversing its digits increases the number by 18 Set up the relational equation [10x + (16-x)] + 18 = 10(16 - x) + x Solving for x 9x + 34 = 160 - 9x Combine like terms 18x = 126 Divide each side of the equation by 18 18x/18 = 126/18 x = 7 So 16 - x = 16 - 7 = 9 The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up. The number in our answer is [B]79[/B]

The sum of the squares of two consecutive positive integers is 61. Find these two numbers. Let the 2 consecutive integers be x and x + 1. We have: x^2 + (x + 1)^2 = 61 Simplify: x^2 + x^2 + 2x + 1 = 61 2x^2 + 2x + 1 = 61 Subtract 61 from each side: 2x^2 + 2x - 60 = 0 Divide each side by 2 x^2 + x - 30 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL], we get: x = 5 and x = -6 The question asks for [I]positive integers[/I], so we use [B]x = 5. [/B]This means the other number is [B]6[/B].

Let the 3 integers be x, y, and z. y = x + 1 z = y + 1, or x + 2. Set up our equation: x + (x + 1) + (x + 2) = 42 Group our variables and constants: (x + x + x) + (1 + 2) = 42 3x + 3 = 42 Subtract 3 from each side: 3x = 39 Divide each side of the equation by 3: [B]x = 13 So y = x + 1 = 14 z = x + 2 = 15 (x,y,z) = (13,14,15)[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]

The sum of two y and the quantity of three plus y plus twice the quantity two y minus two equals fifteen The sum of two y and the quantity of three plus y 2y + (3 + y) twice the quantity two y minus two 2(2y - 2) The sum of two y and the quantity of three plus y plus twice the quantity two y minus two 2y + (3 + y) + 2(2y - 2) Equals 15 to get our algebraic expression [B]2y + (3 + y) + 2(2y - 2) = 15[/B] [B][/B] If the problem asks you to solve for yL 2y + 3 + y + 4y - 4 = 15 Group like terms: 7y - 1 = 15 Add 1 each side: 7y = 16 Divide each side by 7: y = [B]16/7[/B]

the sum of w and v divided by their difference the sum of w and v: w + v their difference: w - v the sum of w and v divided by their difference [B](w + v)/(w - v)[/B]

the sum of x and 3 is divided by 2 The sum of x and 3 x + 3 Divide this expression by 2 (x + 3)/2

the sum of X and 3 is divided by 2 The sum of X and 3 X + 3 Is divided by 2 [B](X + 3)/2[/B]

the sum of x and 96 equals half of x half of x means we divide x by 2: x/2 The sum of x and 96: x + 96 The phrase equals means we set x + 96 equal to x/2: [B]x + 96 = x/2[/B]

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the length of the trunk Let p be the top part of the tree. We have p = 3t. Divide by 3, we get t = [B]p/3[/B]

the total of a and 352 equals a divided by 195 Take this algebraic expression in 3 parts: [LIST=1] [*]The total of a and 352 means we add 352 to a: a + 352 [*]a divided by 195: a/195 [*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression: [/LIST] [B]a + 352 = a/195[/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]

There are 100 teachers in a school of 3300 students find the ratio of number of teachers to the number of students. The Ratio is 100/3300. Divide top and bottom by 100: 1/330 or [B]1:33 [/B] You can also this into the search engine: [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A3300&rs=+7%3A5&rtot=+36&ab=+7%3A3&bc=+2%3A5&pl=Simplify+Ratio']Ratio of 100 to 3300[/URL].

120/3/4 = x/6 Cross multiply: 0.75x = 720 Divide each side of the equation by 0.75 [B]x = 960[/B]

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there? Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens: (1) c + p = 13 (2) 2c + 4p = 40 [U]Rearrange (1) to solve for c by subtracting p from both sides:[/U] (3) c = 13 - p [U]Substitute (3) into (2)[/U] 2(13 - p) + 4p = 40 26 - 2p + 4p = 40 [U]Combine p terms[/U] 2p + 26 = 40 [U]Subtract 26 from each side:[/U] 2p = 14 [U]Divide each side by 2[/U] [B]p = 7[/B] [U]Substitute p = 7 into (3)[/U] c = 13 - 7 [B]c = 6[/B] For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]

There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers? Let x be the first integer. y = x + 1 is the next integer. We have the following givens: [LIST=1] [*]2x + y = 16 [*]y = x + 1 [/LIST] Substitute (2) into (1) 2x + (x + 1) = 16 Combine x terms 3x + 1 = 16 Subtract 1 from each side 3x = 15 Divide each side by 3 [B]x = 5[/B] So the other integer is 5 + 1 = [B]6[/B]

There are 2 piles of papers on a desk. Each pile has the same number of papers. There are 12 papers in all on the desk. How many papers are in each pile? 12 papers on the desk / 2 piles of papers Divide top and bottom by 2 [B]6 papers per pile.[/B]

There are 32 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital? 3:8 = x:32 3/8 = x/32 Cross multiply: 8x = 96 Divide each side by 8 x = 12 Check our work: 12:32 Divide each part by 4 12/4 = 3 and 32/4 = 8 so we have 3:8 :)

There are 72 boys and 90 girls on the Math team For the next math competition Mr Johnson would like to arrange all of the students in equal rows with only girls or boys in each row with only girls or boys in each row. What is the greatest number of students that can be put in each row? To find the maximum number (n) of boys or girls in each row, we want the GCF (Greatest Common Factor) of 72 and 90. [URL='https://www.mathcelebrity.com/gcflcm.php?num1=72&num2=90&num3=&pl=GCF+and+LCM']Using our GCF calculator for GCF(72,90)[/URL], we get 18. [LIST] [*]72 boys divided by 18 = [B]4 rows of boys[/B] [*]90 girls divided by 18 = [B]5 rows of girls[/B] [/LIST]

There are 8 lions, 4 tigers, 5 cheetahs, 6 giraffes, 7 hippos, and 78 monkeys at the City Zoo. If each of the 4 zookeepers feeds the same number of animals, how many animals does each zookeeper feed? Calculate Total Animals: 8 + 4 + 5 + 6 + 7 + 78 = 108 Now divide 108 animals equally into 4 zookeepers 108/4 = [B]27 animals each zookeeper will feed[/B]

[SIZE=6]There are 812 students in a school. There are 36 more girls than boys. How many girls are there? Let b be boys Let g be girls We're given two equations:[/SIZE] [LIST=1] [*][SIZE=6]b + g = 812[/SIZE] [*][SIZE=6]g = b + 36[/SIZE] [/LIST] [SIZE=6]Rearrange equation 2 to subtract b from each side: [/SIZE] [LIST=1] [SIZE=6] [LIST][*]b + g = 812[/LIST] [LIST][*]-b + g = 36[/LIST][/SIZE] [/LIST] [SIZE=6]Add equation (1) to equation (2): b - b + 2g = 812 + 36 The b's cancel: 2g = 848 Divide each side by 2: 2g/2 = 848/2 g = [B]424[/B] [B][/B] To find b, we put g= 424 into equation 1: b + 424 = 812 b = 812 - 424 b = [B]388[/B] [MEDIA=youtube]JO1b7qVwWoI[/MEDIA] [/SIZE]

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers. Let the first number be x and the second number be y. We have 2 equations: [LIST=1] [*]4x + 3y = 24 [*]2x - 3y = 24 [/LIST] Without doing anything else, we can add the 2 equations together to eliminate the y term: (4x + 2x) + (3y - 3y) = (24 + 24) 6x = 48 Divide each side by 6: [B]x = 8 [/B] Substitute this into equation (1) 4(8) + 3y = 24 32 + 3y = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].

Set up two equations: (1) b = g + 16 (2) b + g = 150 Substitute equation (1) into (2) (g + 16) + g = 150 Combine like terms 2g + 16 = 150 Subtract 16 from each side 2g = 134 Divide each side by 2 to isolate g g = 67 Substitute this into equation (1) b = 67 + 16 [B]b = 83[/B]

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number Let's call our number n. Double the number means we multiply n by 2: 2n Subtract 6 from the result means we subtract 6 from 2n: 2n - 6 Divide the answer by 2: (2n - 6)/2 We can simplify this as n - 3 The quotient will be 20. This means the simplified term above is set equal to 20: [B]n - 3 = 20 [/B] <-- This is our algebraic expression If you want to take it a step further, and solve for n in the algebraic expression above, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-3%3D20&pl=Solve']type this expression into our calculator[/URL], and get: n = 23

Thirty is half of the sum of 4 and a number. The phrase [I]a number[/I] represents an arbitrary variable, let's call it x. The sum of 4 and a number: 4 + x Half of this sum means we divide by 2: (4 + x)/2 Set this equal to 30: [B](4 + x)/2 = 30[/B] <-- This is our algebraic expression

triple 5, raise the result to the 10th power, then divide p by what you have Triple 5, means multiply 5 by 3 3 * 5 --> Simplified, this is 15 Raise the result to the 10th power, means we raise 15 to the 10 power: 15^10 Then divide it by p: [B]15^10/p[/B]

triple c divide the result by a Take this algebraic expression in pieces. Triple c means we multiply the variable c by 3 3c Divide the result by a, means we take 3c, and divide by a [B]3c/a[/B]

triple s add the result to q then divide what you have by r. Triple s means multiply s by 3: 3s Add the result to q: 3s + q Divide what you have by r: [B](3s + q)/r[/B]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. Twice a number: 2x decreased by eight 2x - 8 [I]is [/I]means equal to. Set 2x - 8 equal to zero for our algebraic expression: [B]2x - 8 = 0 [/B] If the problem asks you to solve for x, add 8 to each side: 2x = 8 Divide each side by 2: x= [B]4[/B]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour? Set up two equations: (1) 10x + 5y = 1225 (2) x + y = 170 Rearrange (2) x = 170 - y Substitute that into (1) 10(170 - y) + 5y = 1225 1700 - 10y + 5y = 1225 1700 - 5y = 1225 Move 5y to the other side 5y + 1225 = 1700 Subtract 1225 from each side 5y =475 Divide each side by 5 [B]y = 95[/B] Which means x = 170 - 95, [B]x = 75[/B]

Two numbers total 50 and have a difference of 28. Find the two numbers. Using x and y as our two numbers, we write the following 2 equations: [LIST=1] [*]x + y = 50 [*]x - y = 28 [/LIST] Add the 2 rows: 2x = 78 Divide each side by 2: [B]x = 39[/B] If x = 39, then from (1), we have y = 50 - 39 [B]y = 11[/B]

Let the numbers be x and y. Set up our givens: [LIST=1] [*]x + y = 83 [*]x - y = 17 [/LIST] [U]Add equation (1) to equation (2)[/U] x + x + y - y = 83 + 17 [U]The y-terms cancel out:[/U] 2x = 100 [U]Divide each side by 2:[/U] 2x/2= 100/2 x = [B]50[/B] [U] Plug x = 50 into equation (1)[/U] 50 + y = 83 [U]Subtract 50 from each side:[/U] 50 - 50 + y = 83 - 50 [U]Cancel the 50 on the left side:[/U] y = [B]33 [/B] So our two numbers (x, y) = (33, 50) [MEDIA=youtube]jajO043ChUM[/MEDIA]

Two years of local internet service costs 685, including the installation fee of 85. What is the monthly fee? Subtract the installation fee of 85 from the total cost of 685 to get the service cost only: 685 - 85 = 600 Now, divide that by 24 months in 2 years to get a per month fee 600/24 = [B]25 per month[/B]

Cross multiply: ub = ak Divide each side of the equation by k to isolate a: a = ub/k [MEDIA=youtube]A3NW3Y68iNY[/MEDIA]

U=ak/b, for a [U]Cross multiply:[/U] Ub = ak [U]Divide each side by k[/U] [B]a = Ub/k[/B]

Free Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, proj_BA and and the vector component of A orthogonal to B → A - proj_BA
Also calculates the horizontal component and vertical component of a 2-D vector.

Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimited rentals. What number of movies rentals is plan B less than plan A? Let x equal the number of movies rented and C the cost for rentals Plan A: C = 1.25x + 25 Plan B: C = 40 Set up the inequality: 1.25x + 25 > 40 Subtract 25 from each side: 1.25x > 15 Divide each side of the inequality by 1.25 x > 12 So [B]13[/B] rentals or more make Plan B less than Plan A.

vw^2+y=x for w This is an algebraic expression. Subtract y from each side: vw^2 + y - y = x - y The y's cancel on the left side, so we're left with: vw^2 = x - y Divide each side by v w^2 = (x - y)/v Take the square root of each side: w = [B]Sqrt((x - y)/v)[/B]

[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute. After how many minutes are there equal volumes of water in the 2 tanks? Write an equation and solve it.[/QUOTE] Tank A: V = 200 - 2x Tank B: V = 100 - 0.5x Where x is the number of minutes passed. Set them equal to each other 200 - 2x = 100 - 0.5x Subtract 100 from each side: 100 - 2x = -0.5x Add 2x to each side: 1.5x = 100 Divide each side of the equation by x: x = 66.66666667

Wendy is paid $7.50 per hour plus a bonus of $80 each week. Last week Wendy earned $312.50. How many hours did Wendy work last week? Setup the earnings equation with h hours: 7.5h + 80 = 312.50 Solve for [I]h[/I] in the equation 7.5h + 80 = 312.50 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 80 and 312.50. To do that, we subtract 80 from both sides 7.5h + 80 - 80 = 312.50 - 80 [SIZE=5][B]Step 2: Cancel 80 on the left side:[/B][/SIZE] 7.5h = 232.5 [SIZE=5][B]Step 3: Divide each side of the equation by 7.5[/B][/SIZE] 7.5h/7.5 = 232.5/7.5 h = [B]31 [URL='https://www.mathcelebrity.com/1unk.php?num=7.5h%2B80%3D312.50&pl=Solve']Source[/URL][/B]

What is the inverse of dividing by 3 [B]Multiplying by 3[/B] Suppose we have 2 divided by 3: 2/3 To undo this operation to get to 2 again, we'd multiply by 3: 2/3 * 3 = 2

What is the ratio 18b^2 to 45b written in simplest for Using our [URL='https://www.mathcelebrity.com/monomial.php?num1=+%286xy%5E3%29%5E4&num2=+%283y%5E4%29%5E5%288x%5E6y%5E3%29&num3=18b%5E2%2F45b&pl=Divide']monomial calculator[/URL], we see that 18b^2/45b is [B]2b/5[/B]

Answer Choices: A. 6 B. 1/2 C. 1/3 D. 1/4 [U]Multiply through by 6:[/U] 2 * 6x/3 + 6/6 = 6/3 4x + 1 = 2 [U]Subtract 1 from each side:[/U] 4x + 1 - 1 = 2 - 1 4x = 1 [U]Divide each side by 4:[/U] 4x/4 = 1/4 x = [B]1/4[/B] [MEDIA=youtube]jywMlPs3c2w[/MEDIA]

What number when multiplied by four exceeds itself by 42? Let the number be n. We have: 4n = n + 42 Subtract n from each side: 3n = 42 Divide each side by 3 [B]n = 14[/B]

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum? Let the 3 consecutive positive integers be: [LIST=1] [*]x [*]x + 1 [*]x + 2 [/LIST] The product is: x(x + 1)(x + 2) The sum is: x + x + 1 + x + 2 = 3x + 3 We're told the product is equivalent to: x(x + 1)(x + 2) = 16(3x + 3) x(x + 1)(x + 2) = 16 * 3(x + 1) Divide each side by (x + 1) x(x + 2) = 48 x^2 + 2x = 48 x^2 + 2x - 48 = 0 Now subtract the sum from the product: x^2 + 2x - 48 - (3x + 3) [B]x^2 - x - 51[/B]

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number means we subtract x from 100: 100 - x The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x 4x + 40 = 100 - x Solve for [I]x[/I] in the equation 4x + 40 = 100 - x [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4x and -x. To do that, we add x to both sides 4x + 40 + x = -x + 100 + x [SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE] 5x + 40 = 100 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 40 and 100. To do that, we subtract 40 from both sides 5x + 40 - 40 = 100 - 40 [SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE] 5x = 60 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5x/5 = 60/5 x = [B]12[/B] Check our work for x = 12: 4(12) + 40 ? 100 - 12 48 + 40 ? 100 - 12 88 = 88

When Ms. Thelma turned on her oven, the temperature inside was 70 degrees F. The temperature began to rise at a rate of 20 degrees per minute. How Long did it take for the oven to reach 350 degrees F? Figure out how many degrees we have left: 350 - 70 = 280 Let m = minutes 20m = 280 Divide each side by m [B]m = 14[/B]

When the circumference of a circle is increased from 10 pi inches to 15 pi inches, by how many inches is the radius increased? C = 2pir Smaller circle: 2pir = 10pi Divide each side by 2pi: r = 5 Larger circle: 2pir = 15pi Divide each side by 2pi: r = 7.5 Difference = 7.5 - 5 = [B]2.5 or 2&1/2 [MEDIA=youtube]HvMNNffcv78[/MEDIA][/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square? Original square side length is s Area = s^2 Double the side lengths to 2s New area = (2s)^2 = 4s^2 Setup the difference relation: 4s^2 - s^2 = 432 3s^2 = 432 Divide each side by 3: 3s^2/3 = 432/3 s^2 = 144 s = [B]12[/B]

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line. If we rearrange A) by subtracting 6x from each side, we get: 2y = -6x + 15 Divide each side by 2, we get: y = -3x + 15/2 This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start? Let the starting candy amount be c. We're given: (c - 5)/3 = 3 Cross multiply: c - 5 = 3*3 c - 5 = 9 [URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get: c = 14

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the cube of w . The constant of proportionality is 8.25 . [LIST] [*]Varies jointly or directly means we multiply [*]Varies inversely means divide [*]The cube of w means we raise w to the 3rd power: w^3 [/LIST] Using k = 8.25 as our constant of proportionality, we have: [B]g = 8.25qt/w^3[/B]

wy - ma = ay/n for y Subtract ay/n from each side: wy - ma - ay/n = ay/n - ay/n wy - ma - ay/n = 0 Now add ma to each side: wy - ay/n = ma Factor out y: y(w - a/n) = ma Divide each side by (w - a/n) y = [B]ma/(w - a/n)[/B]

X divide by 6 subtract by 1 x divide by 6 x/6 subtract by 1 [B]x/6 - 1[/B]

x/y + 9 = n for y First, subtract 9 from each side to isolate the y term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side, and we get: x/y = n - 9 Cross multiply: x = y(n - 9) Divide each side by (n - 9): x/(n - 9) = y(n - 9)/(n - 9) Cancel the (n - 9) on the right side, and we get: y = [B]x/(n - 9)[/B]

Xavier has $132 to buy a video game. Each game costs $12. Write an equation to find the number of games Xavier can purchase. Let g be the number of games, we have a cost function C(g) C(g) = 12g We want to find g such that C(g) = 132 12g = 132 Divide each side by 12 [B]g = 11[/B]

xy divided by 2 [B]xy/2[/B]

Y add z then divide by x y add z: y + z Then divide by x means we divide the sum (y + z) by x [B](y + z)/x[/B]

y varies directly as x and inversely as I Note: Direct variation means we multiply. Inverse variation means we divide. There exists a constant k such that: [B]y = kx/i[/B]

Yolanda runs each lap in 7 minutes. She will run less than 35 minutes today. What are the possible numbers of laps she will run today? 7 minutes per lap must be less than 35 minutes. Let l be the number of laps 7l < 35 Divide each side by 7 [B]l < 5[/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save? [U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U] (1) s + 75w =950 (2) s + 50w = 800 [U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U] (3) s = 950 - 75w [U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U] (4) s = 800 - 50w [U]Set (3) and (4) equal to each other so solve for w[/U] 950 - 75w = 800 - 50w [U]Add 75w to each side, and subtract 950 from each side:[/U] 25w = 150 [U]Divide each side by w[/U] [B]w = 6[/B] Now plug w = 6 into (3) s = 950 - 75(6) s = 950 - 450 [B]s = 500[/B]

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt. We have I = 2, P = 25, t = 0.5 2 = 25(r)0.5 Divide each side by 0.5 4 = 25r Divide each side by 25 r = 4/25 [B]r = 0.16[/B] As a percentage, this is [B]16%[/B]

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Subtract the cost of the magazine from what you spent: $25 - $5 = $20. If you spent $20 on 4 erasers, we divide 20/4 = [B]$5 per eraser[/B]

You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile? Set up cost equations: Daily entrance fee: 3d where d is the number of days of membership Membership fee 82 + 1d Set them equal to each other 82 + 1d = 3d Subtract d from each side: 2d = 82 Divide each side by 2 [B]d = 41[/B]

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest? The simple interest formula for the accumulated balance is: Prt = I We are given P = 2,000, r = 0.04, and I = 500. 2000(0.04)t = 500 80t = 500 Divide each side by 80 t = [B]6.25 years [MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]

If you have $6 left over, then 8 notebooks cost $22 - $6 = $16. 8 notebooks = $16 Divide each side of the equation by 8 Each notebook is $2

You have $10.00 to spend on tacos. Each taco costs $0.50. Write and solve an inequality that explains how many tacos you can buy. Let's start with t as the number of tacos. We know that cost = price * quantity, so we have the following inequality for our taco spend: [B]0.5t <= 10 [/B] Divide each side of the inequality by 0.5 to isolate t: 0.5t/0.5 <= 10/0.5 Cancel the 0.5 on the left side and we get: t <= [B]20 [MEDIA=youtube]yy51EsGi1nM[/MEDIA][/B]

You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund Fund A and Fund B to produce an annual interest income of $14,750? You should invest $______in Fund A and $___________in Fund B. Equation is x(.079) + (250,000 - x).054 = 14,750 .025x + 13,500 = 14,750 .025x = 1,250 [B]x = 50,000 for Fund A[/B] So at 5.4%, we have 250,000 - 50,000 = [B]200,000[/B] for the other fund B.

You have $37 to plant garden. If you spend $12.25 on seeds, how many packs of vegetable plants can you buy for 2.75 each? [U]How much do we have to spend on plants?[/U] $37 - 12.25 = $24.75 [U]Calculate how many vegetable plants we can buy. Set up an equation where x = vegetable plants[/U] 2.75x = 24.75 Divide each side by 2.75 [B]x = 9[/B]

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Let m be the math problems and s be the science problems. We have two equations: (1) m + s = 42 (2) m = s + 10 Substitute (2) into (1) (s + 10) + s = 42 Combine like terms 2s + 10 = 42 Subtract 10 from each side 2s = 32 Divide each side by 2 [B]s = 16[/B] So that means m = 16 + 10 --> [B]m = 26 (m, s) = (26, 16)[/B]

your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it take you to make $80000? Let y be the number of years of compounding the 2% raise. Since 2% as a decimal is 0.02, we have the following equation for compounding the salary: 45000 * (1.02)^y = 80000 Divide each side by 45000: (1.02)^y = 1.77777777778 To solve this equation for y, we [URL='https://www.mathcelebrity.com/natlog.php?num=1.02%5Ey%3D1.77777777778&pl=Calculate']type it in our search engine[/URL] and we get: y = [B]29.05[/B] [B]Or just over 29 years[/B]

z = (x + y)/mx; Solve for x Cross multiply: zmx = x + y Subtract x from each side zmx - x = y Factor out x x(zm - 1) = y Divide each side by zm - 1 x = y/(zm - 1) [MEDIA=youtube]ksxCS3YlCwY[/MEDIA]

z varies directly with x and inversely with y [LIST] [*]The phrase directly means we multiply. [*]The phrase inversely means we divide [*]Variation means there exists a constant k such that: [/LIST] [B]z = kx/y[/B]

z/w=x+z/x+y for z This is a literal equation. Let's isolate z on one side. Subtract z/x from each side. z/w - z/x = x + y Factor our z on the left side: z(1/w - 1/x) = x + y Divide each side by (1/w - 1/x) z = x + y/(1/w - 1/x) To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw (x - w)/xw Then multiply x + y by the reciprocal z = [B](x + y)xw/(x - w)[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies? Let d = every 2 days. We set up the exponential equation 2 * 2^d = 600,000 Divide each side by 2: 2^d = 300000 To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get d = 18.19 (2 day periods) 18.19 * days per period = 36.38 total days Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].

zy-dm=ky/t for y Isolate terms with y to solve this literal equation. Subtract zy from each side: zy - dm - zy = ky/t - zy Cancel the zy terms on the left side, we get: -dm = ky/t - zy Factor out y: y(k/t - z) = -dm Divide each side by (k/t - z) y = -dm/(k/t - z) (k/t - z) can be rewritten as (k - tz)/t We multiply -dm by the reciprocal of this quotient to get our simplified literal equation: y = [B]-dmt/(k - tz)[/B]

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