19 decreased by the absolute value of c Take this algebraic expression in parts: [LIST] [*]Absolute value of c: |c| [*]19 decreased by the absolute value of c is found by subtracting |c| from 19 [/LIST] [B]19 - |c|[/B]

2 numbers that add up makes 5 but multiplied makes -36 Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x + y = 5 [*]xy = -36 [/LIST] Rearrange equation (1) by subtracting y from each side: [LIST=1] [*]x = 5 - y [*]xy = -36 [/LIST] Substitute equation (1) for x into equation (2): (5 - y)y = -36 5y - y^2 = -36 Add 36 to each side: -y^2 + 5y + 36 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get: y = ([B]-4, 9[/B]) We check our work for each equation: [LIST=1] [*]-4 + 9 = -5 [*]-4(9) = -36 [/LIST] They both check out

31,29,24,22,17 what comes next We see that each sequence term alternates between subtracting 2 and subtracting 5. Since the last term, 17, was found by subtracting 5, our next term is found by subtracting 2 from 17: 17 - 2 = [B]15[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of kids be k [/LIST] Given with assumptions: [LIST=1] [*]a + k = 508 [*]2a + 1.25k = 885.50 (since cost = price * quantity) [/LIST] Rearrange equation (1) by subtracting c from each side to isolate a: [LIST=1] [*]a = 508 - k [*]2a + 1.25k = 885.50 [/LIST] Substitute equation (1) into equation (2): 2(508 - k) + 1.25k = 885.50 Multiply through: 1016 - 2k + 1.25k = 885.50 1016 - 0.75k = 885.50 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]174[/B] Now, to solve for a, we substitute k = 174 into equation 1 above: a = 508 - 174 a = [B]334[/B]

8 is subtracted from the square of x Take this algebraic expression in parts: [LIST] [*]The square of x means we raise x to the power of 2: x^2 [*]8 subtracted from the square of x is found by subtracting 8 from x^2 [/LIST] [B]x^2 - 8[/B]

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in terms of x Piece 1 + Piece 2 = 9 Piece 1 = x x + Piece 2 = 9 Subtracting x from each side, we get: x - x + Piece 2 = 9 - x Cancel the x's on the left side, we get: Piece 2 = [B]9 - x [/B] Check our work: x + 9 - x ? 9 9 = 9

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours? [LIST] [*]The key phrase here is [I]without replacement[/I]. [*]First, it's easier to find the probability of both colors matching, and then subtracting that from 1. [/LIST] We want 1 - (P(Red-Red) + P(Green-Green) + P(White-White)). So we have the following: [U]Find the probability of both colors matching[/U] P(Red-Red) = 10/26 * 9/25 = 0.138462 P(Green-Green) = 10/26 * 9/25 = 0.138462 P(White-White) = 6/26 * 5/25 = 0.046154 P(Red-Red) + P(Green-Green) + P(White-White) = 0.13846 + 0.13846 + 0.046154 = 0.3231 Now, we want to take the complement of this probability which is no colors matching, so we have: P(Both Different Colors) = 1 - P(Same Colors) P(Both Different Colors) = 1 - 0.3231 P(Both Different Colors) = [B]0.6769[/B]

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d + s = 209 [/LIST] We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides: d + s - s = 209 - s Cancel the s's, we get: d = 209 - s So we have the following system of equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d = 209 - s [/LIST] Substitute equation (2) into equation (1) for d: 2(209 - s) + 6.50s = 836.50 Multiply through to remove the parentheses: 418 - 2s + 6.50s = 836.50 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]: s = [B]93[/B]

A football team gained 8 yards on a first down, lost 12 yards on the second down, and gained 16 yards on the third down. How many yards did the team gain or lose? Assumptions: [LIST] [*]We reflect gains by adding [*]We reflect losses by subtracting [/LIST] Plays: [LIST] [*]Gain of 8 = +8 [*]Loss of 12 = -12 [*]Gain of 16 = +16 [/LIST] Net Gain/Loss +8 - 12 + 16 [B]+12 (gain)[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: [LIST=1] [*]m = w + 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Rearrange equation 1 in terms of w my subtracting 5 from each side: [LIST=1] [*]w = m - 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Substitute equation (1) and equation (2) into equation (3) 0.5m + m + m - 5 = 100 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]42 [/B] Now, substitute m = 42 into equation 2 to solve for d: d = 0.5(42) d = [B]21 [/B] Now substitute m = 42 into equation 1 to solve for w: w = 42 - 5 w = [B]37 [/B] To summarize our ages: [LIST] [*]Man (m) = 42 years old [*]Daughter (d) = 21 years old [*]Wife (w) = 37 years old [/LIST]

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe is left? Calculate the length of cut pipe: 4 pieces * 33 inches per piece = 132 inches The remaining pipe is found by subtracting the original pipe length by the cut pipe length: 144 - 132 = [B]12 inches[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? [LIST] [*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. [*]This expression must be less than 12. [/LIST] [U]Setup the inequality:[/U] 1.5 + 0.8x < 12 [U]Subtracting 1.5 from each side of the inequality[/U] 0.8x < 10.5 [U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U] [B]x < 13.125[/B]

A+B+D=255 B+15=A D+12=B A= [LIST=1] [*]A + B + D = 255 [*]B + 15 = A [*]D + 12 = B [*]A = ? [*]Rearrange (3) to solve for D by subtracting 12 from each side: D = B - 12 [/LIST] Substitute (2) and (5) into 1 (B + 15) + B + (B - 12) = 255 Combine like terms: 3B + 3 = 255 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3b%2B3%3D255&pl=Solve']equation solver[/URL], b = 84 Substitute b = 84 into equation (2): A = 84 + 15 [B]A = 99[/B]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair Let the number of students be s and the others be o. We're given two equations: [LIST=1] [*]o + s = 2848 [*]3.75o + 2.50s = 10078.75 [/LIST] Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s [LIST=1] [*]o = 2848 - s [*]3.75o + 2.50s = 10078.75 [/LIST] Now substitute equation 1 into equation 2: 3.75(2848 - s) + 2.50s =10078.75 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]481[/B]

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much as 7,500 bottles. What is the maximum and minimum expected production at the bottling company? Our production amount p is found by adding and subtracting our variance amount: 215,000 - 7,500 <= p <= 215,000 + 7,500 [B](min) 207,500 <= p <=222,500 (max)[/B]

Free Basic Math Operations Calculator - Given 2 numbers, this performs the following arithmetic operations:
* Addition (Adding) (+)
* Subtraction (Subtracting) (-)
* Multiplication (Multiplying) (x)
* Long division (Dividing) with a remainder (÷)
* Long division to decimal places (÷)
* Partial Sums (Shortcut Sums)
* Short Division
* Duplication and Mediation

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax Let the original price be p. p Apply 25% discount first, which is the same as subtracting 0.25: p(1 - 0.25) Subtract 30 for in store buck p(1 - 0.25) - 30 The phrase [I]no more than[/I] means an inequality using less than or equal to: p(1 - 0.25) - 30 <= 60 To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get: [B]p <= 120[/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]

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level. Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following: 1,684 - (-216) Since subtracting a negative is a positive, we have: 1,684 + 216 [B]1,900 feet[/B]

Free Fractions and Mixed Numbers Calculator - Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:
* Addition (Adding)
* Subtraction (Subtracting)
* Positive Difference (Absolute Value of the Difference)
* Multiplication (Multiplying)
* Division (Dividing: complex fraction division is included)
* Compare Fractions
* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).
* Reciprocal of a Fraction
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If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions. Convert 2 to a fraction with a denominator of 10: 20/2 = 10, so we multiply 2 by 10/10: 2*10/10 = 20/10 Add 2 to the numerator and denominator: (n + 2)/(d + 2) = 9/10 Cross multiply and simplify: 10(n + 2) = 9(d + 2) 10n + 20 = 9d + 18 Move constants to right side by subtracting 20 from each side and subtracting 9d: 10n - 9d = -2 Subtract 3 from the numerator and denominator: (n - 3)/(d - 3) = 4/5 Cross multiply and simplify: 5(n - 3) = 4(d - 3) 5n - 15 = 4d - 12 Move constants to right side by adding 15 to each side and subtracting 4d: 5n - 4d = 3 Build our system of equations: [LIST=1] [*]10n - 9d = -2 [*]5n - 4d = 3 [/LIST] Multiply equation (2) by -2: [LIST=1] [*]10n - 9d = -2 [*]-10n + 8d = -6 [/LIST] Now add equation (1) to equation (2) (10 -10)n (-9 + 8)d = -2 - 6 The n's cancel, so we have: -d = -8 Multiply through by -1: d = 8 Now bring back our first equation from before, and plug in d = 8 into it to solve for n: 10n - 9d = -2 10n - 9(8) = -2 10n - 72 = -2 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=10n-72%3D-2&pl=Solve']plug this equation into our search engine[/URL] and we get: n = 7 So our fraction, n/d = [B]7/8[/B]

if 2z-1 is an odd integer what is the preceding odd integer? The preceding odd integer is found by subtracting 2: 2z - 1 - 2 [B]2z - 3[/B]

If a is an even integer and b is an odd integer then prove a ? b is an odd integer Let a be our even integer Let b be our odd integer We can express a = 2x (Standard form for even numbers) for some integer x We can express b = 2y + 1 (Standard form for odd numbers) for some integer y a - b = 2x - (2y + 1) a - b = 2x - 2y - 1 Factor our a 2 from the first two terms: a - b = 2(x - y) - 1 Since x - y is an integer, 2(x- y) is always even. Subtracting 1 makes this an odd number. [MEDIA=youtube]GDVuQ7bGHx8[/MEDIA]

If Jody had $3 more she would have twice as much as Lars together they have $60. Let j be Jody's money and l be Lars's money. We have two equations: [LIST=1] [*]j + l = 60 [*]j + 3 = 2l [/LIST] Rearrange (2) to solve for j by subtracting 3 j = 2l - 3 Now substitute this into (1) (2l - 3) + l = 60 Combine like terms 3l - 3 = 60 Enter this into our [URL='http://www.mathcelebrity.com/1unk.php?num=3l-3%3D60&pl=Solve']equation calculator[/URL], and we get: [B]l = 21[/B] Now plug l = 21 into our rearranged equation above: j = 2(21) - 3 j = 42 - 3 [B]j = 39[/B]

If n represents an odd integer what represents the previous smaller odd integer Each odd integer is 2 away from the last one, so the previous smaller odd integer is found by subtracting 2 from n: [B]n - 2[/B]

If p+4=2 and q-3=2, what is the value of qp? Isolate p by subtracting 4 from each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=p%2B4%3D2&pl=Solve']equation calculator[/URL] p = -2 Isolate q by adding 3 to each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=q-3%3D2&pl=Solve']equation calculator[/URL]: q = 5 pq = (-2)(5) [B]pq = -10[/B]

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference in his score on Sunday compared to his score on Saturday Givens and opening thoughts: [LIST] [*]Think of par as 0 or average. [*]Under par is negative [*]Over par is positive [*]We have 4 under par as -4 [*]We have 5 over par as +5 [/LIST] The difference is found by subtracting: +5 - -4 +5 + 4 [B]9 strokes[/B]

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat? Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given: [LIST=1] [*]4s + p = 11.45 [*]5s + 3p + c = 27.41 [*]5s + c = 16.94 [/LIST] Rearrange (1) by subtracting 4s from each side: p = 11.45 - 4s Rearrange (3)by subtracting 5s from each side: c = 16.94 - 5s Take those rearranged equations, and plug them into (2): 5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41 Multiply through: 5s + 34.35 - 12s + 16.94 - 5s = 27.41 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get: [B]s = 1.99 [/B] <-- Shirt Cost Plug s = 1.99 into modified equation (1): p = 11.45 - 4(1.99) p = 11.45 - 7.96 [B]p = 3.49[/B] <-- Slacks Cost Plug s = 1.99 into modified equation (3): c = 16.94 - 5(1.99) c = 16.94 - 9.95 [B]c = 6.99[/B] <-- Sports Coat cost

Giving away 2 means subtracting, so we have 10 - 2 = 8 pens left over.

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 and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type? Let d be dimes and q be quarters. Set up two equations from our givens: [LIST=1] [*]d + q = 41 [*]0.1d + 0.25q = 7.85 [/LIST] [U]Rearrange (1) by subtracting q from each side:[/U] (3) d = 41 - q [U]Now, substitute (3) into (2)[/U] 0.1(41 - q) + 0.25q = 7.85 4.1 - 0.1q + 0.25q = 7.85 [U]Combine q terms[/U] 0.15q + 4.1 = 7.85 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U] [B]q = 25[/B] [U]Substitute q = 25 into (3)[/U] d = 41 - 25 [B]d = 16[/B]

Look at this sequence: 53, 53, 40, 40, 27, 27, ... What number should come next? This looks like a sequence where we subtract 13 and then 0, 13 and then 0 from the prior number. Since the last group of 27 repeated, our next number is found by subtracting 13: 27 - 13 = [B]14[/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]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number The phrase [I]a number [/I]means an arbitrary variable, let's call it x. multiply a number by 6 and subtract 6: 6x - 6 Multiply a number by 3 and subtract 4: 3x - 4 The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4 6x - 6 = 3x - 4 To solve this equation for x, we type it in our search engine and we get: x = [B]2/3[/B]

On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau? Difference is found by subtracting the lower temperature from the higher temperature: [URL='https://www.mathcelebrity.com/longdiv.php?num1=109&num2=63&pl=Subtract']109 - 63 [/URL]= [B]46[/B]

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith? Assumptions: [LIST] [*]Let b be the number of hours Giselle worked as a blacksmith [*]Let c be the number of hours Giselle worked as a carpenter [/LIST] Givens: [LIST=1] [*]b + c = 30 [*]25b + 20c = 690 [/LIST] Rearrange equation (1) to solve for b by subtracting c from each side: [LIST=1] [*]b = 30 - c [*]25b + 20c = 690 [/LIST] Substitute equation (1) into equation (2) for b 25(30 - c) + 20c = 690 Multiply through: 750 - 25c + 20c = 690 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get: c = [B]12 [/B] Now, we plug in c = 12 into modified equation (1) to solve for b: b = 30 - 12 b = [B]18[/B]

Subtracting 9s shortcut Add the digits of the larger number [LIST] [*]10 - 9 = 1 + 0 = 1 [*]11 - 9 = 1 + 1 = 2 [*]12 - 9 = 1 + 2 = 3 [*]13 - 9 = 1 + 3 = 4 [*]14 - 9 = 1 + 4= 5 [*]15 - 9=. 1 + 5 = 6 [*]16 - 9 = 1 + 6= 7 [*]17 - 9= 1 + 7 = 8 [*]18 - 9 = 1 + 8 = 9 [*]19 - 9 = 1 + 9 = 10 [/LIST] [MEDIA=youtube]YOHcJ6UG1D8[/MEDIA]

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers. Let the first number be x. The second number is y. We have: [LIST=1] [*]x + y = 18 [*]3x = 4y + 5 [/LIST] Rearrange (2), by subtracting 4y from each side: 3x - 4y = 5 So we have a system of equations: [LIST=1] [*]x + y = 18 [*]3x - 4y = 5 [/LIST] Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]x = 11 y = 7[/B]

the sum of 2 times a number and -2, added to 4 times a number. The phrase, [I]a number[/I], means an arbitrary variable, let's call it x. 2 times a number 2x The sum of means add, so we add -2, which is the same as subtracting 2 2x - 2 Now, we add 4 times x 2x - 2 + 4x Combining like terms, we have: (2 + 4)x - 2 [B]6x - 2[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get: l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: [LIST=1] [*]x + y = 10 [*]10x+ y = 15y + 4 [/LIST] Simplifying Equation (2) by subtracting y from each side, we get: 10x = 14y + 4 Rearranging equation (1), we get: x = 10 - y Substitute this into simplified equation (2): 10(10 - y) = 14y + 4 100 - 10y = 14y + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get: y = 4 Plug this into rearranged equation (1), we get: x = 10 - 4 x = 6 So our number xy is [B]64[/B]. Let's check our work against equation (1): 6 + 4 ? 10 10 = 10 Let's check our work against equation (2): 10(6)+ 4 ? 15(4) + 4 60 + 4 ? 60 + 4 64 = 64

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: [LIST=1] [*]a + h + c = 48 [*]a = 0.5h [*]a = c + 4 [/LIST] To isolate equations in terms of Suresh's age (a), let's do the following: [LIST] [*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4 [*]Rewriting (2) by multiply each side by 2, we have h = 2a [/LIST] We have a new system of equations: [LIST=1] [*]a + h + c = 48 [*]h = 2a [*]c = a - 4 [/LIST] Plug (2) and (3) into (1) a + (2a) + (a - 4) = 48 Group like terms: (1 + 2 + 1)a - 4 = 48 4a - 4 = 48 [URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 13 [/B]<-- Suresh's age This means that Hakima's age, from modified equation (2) above is: h = 2(13) [B]h = 26[/B] <-- Hakima's age This means that Saad's age, from modified equation (3) above is: c = 13 - 4 [B]c = 9[/B] <-- Saad's age [B] [/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]

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the larger? Let x and y be consecutive integers, where y = x + 1 We have 7x < 6y as our inequality. Substituting x, y = x + 1, we have: 7x < 6(x + 1) 7x < 6x + 6 Subtracting x from each side, we have: x < 6, so y = 6 + 1 = 7 (x, y) = (6, 7)

When five people are playing a game called hearts, each person is dealt ten cards and the two remaining cards are put face down on a table. Because of the rules of the game, it is very important to know the probability of either of the two cards being a heart. What is the probability that at least one card is a heart? Probability that first card is not a heart is 3/4 since 4 suits in the deck, hearts are 1/4 of the deck. Since we don't replace cards, the probability of the next card drawn without a heart is (13*3 - 1)/51 = 38/51 Probability of both cards not being hearts is found by multiplying both individual probabilities: 3/4 * 38/51 = 114/204 Having at least one heart is found by subtracting this from 1 which is 204/204: 204/204 - 114/204 = 90/204 [URL='https://www.mathcelebrity.com/search.php?q=90%2F204&x=0&y=0']This reduces to[/URL] [B]15/34[/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].

x + 8y/4 = 9y for x Step 1: Isolate x by subtracting 8y/4 from each side: x + 8y/4 - 8y/4 = 9y - 8y/4 Cancel 8y/4 on the left side: x =[B] 9y - 8y/4 [MEDIA=youtube]5NLDNw_T8GU[/MEDIA][/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]

Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find how much he can spend for everything else. Let x be the amount your brother can spend. Subtracting the cost of the plane ticket from savings, we have: x <= 2000 - 637 [B]x <= 1,363[/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase? Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations: [LIST=1] [*]c + f = 10 [*]c + 1.5f = 12.50 [/LIST] Rearrange equation 1 by subtracting f from both sides: [LIST=1] [*]c = 10 - f [*]c + 1.5f = 12.50 [/LIST] Substitute equation (1) into equation (2): 10 - f + 1.5f = 12.50 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get: [B]f = 5[/B] Now, substitute this f = 5 value back into modified equation (1) above: c = 10 - 5 [B]c = 5[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x): [U]She subtracts 6 then multiplies the result by 5[/U] [LIST] [*]Subtract 6: x - 6 [*]Multiply the result by 5: 5(x - 6) [/LIST] [U]She subtracts 5 from the number then multiplying by 4[/U] [LIST] [*]Subtract 6: x - 5 [*]Multiply the result by 5: 4(x - 5) [/LIST] Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation: 5(x - 6) = 4(x - 5) Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]10[/B]