-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]

2x plus 4 increased by 15 is 57 Take this algebraic expression in parts: [LIST] [*]2x plus 4: 2x + 4 [*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19 [*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57: [/LIST] Our final algebraic expression is: [B]2x + 19 = 57 [/B] To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get x = [B]19[/B]

3, 8, 13, 18, .... , 5008 What term is the number 5008? For term n, we have a pattern: f(n) = 5(n - 1) + 3 Set this equal to 5008 5(n - 1) + 3 = 5008 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=5%28n-1%29%2B3%3D5008&pl=Solve']equation solver,[/URL] we get: n = [B]1002[/B]

54 is the sum of 15 and Vidyas score. Let Vida's score be s. The sum of 15 and s: s + 15 When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below: [B]s + 15 = 54 [/B] To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving. The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16: d + 16 The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59 d + 16 = 59 <-- [B]This is our algebraic expression[/B] Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]: d = [B]43[/B]

8 years from now a girls age will be 5 times her present age whats is the girls age now. Let the girl's age now be a. We're given: a + 8 = 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 2[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils. Removed means we subtract from the total. So Our equation is: x - 6 = 54 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get: x = [B]60[/B]

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be? Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece: [LIST=1] [*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer) [*]m = s + 6 [*]s + m + l = 57 [/LIST] We substitute equations (1) and (2) into equation (3): s + (s + 6) + (s + 9) = 57 Group like terms: (1 + 1 + 1)s + (6 + 9) = 57 3s + 15 = 57 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]14 [/B] [U]Plug s = 14 into equation 2 to solve for m:[/U] m = 14 + 6 m = [B]20 [/B] [U]Plug s = 14 into equation 1 to solve for l:[/U] l = 14 + 9 l = [B]23 [/B] Check our work for equation 3: 14 + 20 + 23 ? 57 57 = 57 <-- checks out [B][/B]

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides? We set up our inequality using less than or equal to, since our cash is capped at $50. We use S for our : Cost per ride * r + Admission <= 50 Plugging in our numbers, we get: 2.50r + 6 <= 50 [B][/B] Now, if the problem asks you to put this in terms of r, then [URL='https://www.mathcelebrity.com/1unk.php?num=2.50r%2B6%3C%3D50&pl=Solve']we plug this inequality into our search engine[/URL] and we get: r <= 17.6 Since we cannot do fractional rides, we round down to 17: [B]r <= 17[/B]

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55. [U]The cost function for "u" uniforms C(u) is given by:[/U] C(u) = Cost per uniform * u + Fixed Costs [B]C(u) = 15u + 640[/B] Build the revenue function R(u) where u is the number of uniforms: R(u) = Sale Price per uniform * u [B]R(u) = 55u[/B] Calculate break even function: Break even is where Revenue equals cost C(u) = R(u) 15u + 640 = 55u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]16 So we break even selling 16 uniforms[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000? [U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U] C(t) = Variable Cost * t + Fixed Costs C(t) = 84t + 110000 [U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U] R(t) = Sale Price * t R(t) = 132t [U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U] P(t) = R(t) - C(t) P(t) = 132t - (84t + 110000) P(t) = 132t - 84t - 110000 P(t) = 48t - 110000 [U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U] 48t - 110000 = 560000 [U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U] t =[B] 13,958.33 If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy? Let p be the purchase price of pigs. We're given: [LIST] [*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C. [*]5 of them died, so he has p - 5 left [*]He sells 4(p - 5) pigs for a revenue amount R [*]Since profit is Revenue - Cost, which equals 56, we have: [/LIST] Calculate Profit P = R - C Plug in our numbers: 4(p - 5) - 232 = 56 4p - 20 - 232 = 56 To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get: p = [B]77[/B]

a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost of each? Let the cost of the horse be h, and the cost of the saddle be s. We're given: [LIST=1] [*]h + s = 5000 [*]h = 4s [/LIST] Substitute equation (2) into equation (1): 4s + s = 5000 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D5000&pl=Solve']Type this equation into the search engine[/URL], we get: [B]s = 1,000[/B] Substitute s = 1000 into equation (2): h = 4(1000) [B]h = 4,000[/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 parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides? A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below: P = 2l + 2w We're given w = 17 and P = 54. So we plug this into the formula for perimeter: 2l + 2(17) = 54 2l + 34 = 54 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number? Let the rational number be x. We're given: 7x/3 - 3/2 = 92 Using a common denominator of 3*2 = 6, we rewrite this as: 14x/6 - 9/6 = 92 (14x - 9)/6 = 92 Cross multiply: 14x - 9 = 92 * 6 14x - 9 = 552 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]40.07[/B]

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be? Perimeter of a rectangle (P) with length (l) and width (w) is: 2l + 2w = P We're given P = 506 and w = 100. We plug this in to the perimeter formula and get: 2l + 2(100) = 506 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get: l = [B]153[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get: w = [B]7 [/B] To solve for l, we substitute w = 7 into equation (1): l = 3(7) l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. We're given the following: [LIST] [*]l = 3w [/LIST] We know the Perimeter (P) of a rectangle is: P = 2l + 2w Substituting l = 3w and P = 56 into this equation, we get: 2(3w) + 2w = 56 Multiplying through, we get: 6w + 2w = 56 (6 +2)w = 56 8w = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 7[/B] Substitute w = 7 into l = 3w, we get: l = 3(7) [B]l = 21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room. We're given two items: [LIST] [*]l = 3w [*]P = 56 [/LIST] We know the perimeter of a rectangle is: 2l + 2w = P We plug in the given values l = 3w and P = 56 to get: 2(3w) + 2w = 56 6w + 2w = 56 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get: w = [B]7 [/B] To solve for l, we plug in w = 7 that we just found into the given equation l = 3w: l = 3(7) l = [B]21 [/B] So our dimensions length (l) and width (w) are: (l, w) = [B](21, 7)[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room. We're given: l = 3w The Perimeter (P) of a rectangle is: P = 2l + 2w With P = 56, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get: w = [B]7 [/B] Now we plug w = 7 into equation (1) above to solve for l: l = 3(7) l = [B]21[/B]

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car Set up the cost equation C(h) where h is the number of labor hours: C(h) = Labor Cost per hour * h + Parts Cost We're given C(h) = 553, Parts Cost = 265, and Labor Cost per Hour = 48. So we plug these in: 48h + 265 = 553 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=48h%2B265%3D553&pl=Solve']type it in our math engine[/URL] and we get: h = [B]6 hours[/B]

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box? The volume of the box is l x w x h. We're given l and w = 4. So we want height: 56 = 4 x 4 x h 16h = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get: h = [B]3.5[/B]

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains? Distance = Rate x Time Train 1: d = rt t = 1:oo PM to 6:00 PM = 5 hours So we have d = 5r Train 2: d = (r + 30)t t = 3:oo PM to 6:00 PM = 3 hours So we have d = 3(r + 30) Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance: 5r = 3(r + 30) Multiply through: 3r + 90 = 5r [URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed. Train 2's speed = 3(r + 30). Plugging r = 45 into this, we get 3(45 + 30). 3(75) [B]225[/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]

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor Let the number of hours of labor be h. We have the cost function C(h): C(h) = Hourly Labor Rate * h + parts Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have: 75h + 188 = 563 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get: h = [B]5[/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number? The phrase [I]a number[/I] means an arbitrary variable, let's call it n. [LIST] [*]Start with n [*]Add 20 to it: n + 20 [*]Double it means we multiply the expression by 2: 2(n + 20) [*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53 [/LIST] 2(n + 20) = 53 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]6.5[/B]

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank? Let d be the number of dimes, and p be the number of pennies. We're given: [LIST=1] [*]d + p = 50 [*]p = 4d [/LIST] Substitute (2) into (1) d + 4d = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B4d%3D50&pl=Solve']Type that equation into our search engine[/URL]. We get: d = 10 Now substitute this into Equation (2): p = 4(10) [B]p = 40[/B]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now? Let b = Beth's age Let c = Celeste's age We are given: [LIST=1] [*]b = c - 5 [*]b + 1 + c + 1 = 57 [/LIST] Substitute (1) into (2) (c - 5) + 1 + c + 1 = 57 Group like terms: 2c - 3 = 57 [URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B] Substitute c = 30 into Equation (1), we get: b = 30 - 5 [B]b = 25 [/B] Therefore, Beth is 25 and Celeste is 30.

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian? Let Marcus's age be m. Then Brian's age = 3/4m The sum is: m + 3m/4 = 14 Combine like terms 7m/4 = 14 Cross multiply: 7m = 56 [URL='http://www.mathcelebrity.com/1unk.php?num=7m%3D56&pl=Solve']Plugging this into the search engine[/URL], we get m = 8. So Brian's age = 3(8)/4 = 24/4 = 6

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water? This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have: 6m + 16 >= 58 <-- This is our algebraic expression/inequality. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get: [B]m >= 7[/B]

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with? Let the starting amount of cards be s. We're given: [LIST] [*]Dan bought 7 new cards: s + 7 [*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2 [*]Now, he's got 26 cards left. So we set up the following equation: [/LIST] (s + 7)/2 = 26 Cross multiply: s + 7 = 26 * 2 s + 7 = 52 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get: s = [B]45[/B]

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total number of desks in the school was 543. How many classrooms does the school have? Let d be the number of desks per classroom. We're given an equation: 26d + 75 = 543 To solve for d, [URL='https://www.mathcelebrity.com/1unk.php?num=26d%2B75%3D543&pl=Solve']type this equation into our search engine[/URL] and we get: d = [B]18[/B]

Find the largest of three consecutive even integers when six times the first integers is equal to five times the middle integer. Let the first of the 3 consecutive even integers be n. The second consecutive even integer is n + 2. The third (largest) consecutive even integer is n + 4. We are given 6n = 5(n + 2). Multiply through on the right side, and we get: 6n = 5n + 10 [URL='https://www.mathcelebrity.com/1unk.php?num=6n%3D5n%2B10&pl=Solve']Typing 6n = 5n + 10 into the search engine[/URL], we get n = 10. Remember, n was our smallest of 3 consecutive even integers. So the largest is: n + 4 10 + 4 [B]14[/B]

Five times Kim's age plus 13 equals 58. How old is Kim? Let Kim's age be a. We have: Five times Kim's age: 5a Plus 13 means we add 13 5a + 13 Equals 58 means we set the expression 5a + 13 equal to 58 5a + 13 = 58 <-- This is our algebraic expression To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get: a = [B]9[/B]

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number? Let the number be n. We're given two expressions: [LIST=1] [*]Multiply it by 14 and add 13: 14n + 13 [*]Multiply by 5 and add 283: 5n + 283 [/LIST] The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2: 14n + 13 = 5n + 283 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]30[/B]

If Ef = 3x,Fg = 2x,and EG = 5 By segment addition, we have: EF + FG = EG 3x + 2x = 5 To solve for x, we t[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B2x%3D5&pl=Solve']ype this equation into our math engine [/URL]and we get: x = 1 So EF = 3(1) = [B]3[/B] FG = 2(1) = [B]2[/B]

If half the number is added to twice the number, the answer is 50. Let the number be n. Half is also written as 0.5, and twice is written by multiplying by 2. We have: 0.5n + 2n = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.5n%2B2n%3D50&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]n = 20[/B]

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have? Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations: [LIST=1] [*]q = 4n [*]0.25q + 0.05n = 5.25 [/LIST] Substitute equation (1) into equation (2) for q: 0.25(4n) + 0.05n = 5.25 Multiply through and simplify: n + 0.05n = 5.25 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get: n = [B]5 [/B] To get q, we plug in n = 5 into equation (1) above: q = 4(5) q = [B]20[/B]

If y varies inversely as X and Y equals 5 when x equals 2 find X when Y is 4. Using our [URL='http://www.mathcelebrity.com/variation.php?var1=y&cmeth=varies+inversely+as&var2=x&init1=y%3D5&init2=x%3D2&g1=y%3D4&pl=Calculate+Variation']inverse variation calculator[/URL], we get x = 2.5

In 56 years, Stella will be 5 times as old as she is right now. Let Stella's age be s. We're given: s + 56 = 5s [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 14[/B]

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William? [U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U] i = 72+y w = 4+y [U]We want the time for Ishaan age will be 5 times William's age:[/U] i = 5w 72 + y = 5(4 + y) We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get: y = [B]13[/B] [/SIZE]

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left. Let f be the number of Jacks's friends. We have the following equation to represent the chocolates: 3f + 2 = 50 To solve this equation for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=3f%2B2%3D50&pl=Solve']type it in the math engine[/URL] and we get: f = [B]16[/B]

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with? Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below: s + 150 = 500 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get: s = 3[B]50[/B]

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe’s total sales if he earned $507 last week Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by: 0.065s + 325 = 507 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get: s = [B]2800[/B]

John earns $5 mowing lawns. How many hours must he work to earn $40? Let hours worked be h. We have: Earnings = Hourly Rate * Hours Worked 40 = 5h To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=40%3D5h&pl=Solve']type it in our search engine[/URL] and we get: h = [B]8[/B]

Kate spent 1 more than Lauren, and together they spent 5. Let k be the amount Kate spent, and l be the amount Lauren spent. We're given: [LIST=1] [*]k = l + 1 [*]k + l = 5 [/LIST] Substitute (1) into (2): (l + 1) + l = 5 Group like terms 2l + 1 = 5 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B1%3D5&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]l = 2[/B] Plug this into Equation (1), we get: k = 2 + 1 [B]k = 3 [/B] Kate Spent 3, and Lauren spent 2

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit: E(h) = 8h + 1300 The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have: 8h + 1300 >= 5440 To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h%2B1300%3E%3D5440&pl=Solve']type it in our search engine[/URL] and we get: h >= [B]517.5[/B]

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muffin costs $0.75. What’s an equation? Let m be the number of muffins. Cost equals price * quantity, so we have: [B]0.75m = 5.25 [/B] To solve the equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75m%3D5.25&pl=Solve']type the equation into our search engine[/URL] and we get: m = [B]7[/B]

Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each coin does she have? Let n be the number of nickels and q be the number of quarters. We have: [LIST=1] [*]q = n + 12 [*]0.05n + 0.25q = 5.70 [/LIST] Substitute (1) into (2) 0.05n + 0.25(n + 12) = 5.70 0.05n + 0.25n + 3 = 5.70 Combine like terms: 0.3n + 3 = 5.70 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.3n%2B3%3D5.70&pl=Solve']equation calculator[/URL], we get [B]n = 9[/B]. Substituting that back into (1), we get: q = 9 + 12 [B]q = 21[/B]

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal [U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 2h + 8 [U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 5h + 2 [U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U] 2h + 8 = 5h + 2 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2B8%3D5h%2B2&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]2[/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]

Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of 6. If Mr. Wilson paid 54 to park in the garage, for how many hours did he park there? [U]Set up an equation, where f is the flat fee, and h is the number of hours parked:[/U] 3h + f = 54 [U]Substitute f = 6 into the equation:[/U] 3h + 6 = 54 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3h%2B6%3D54&pl=Solve']equation solver[/URL], we get[/U] [B]h = 16[/B]

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for? Set up the cost equation C(h) where h is the number of hours needed to rent the bike: C(h) = Cost per hour * h + rental charge Using our given numbers in the problem, we have: C(h) = 9h + 15 The problem asks for h, when C(h) = 51. 9h + 15 = 51 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B15%3D51&pl=Solve']plug this equation into our search engine[/URL] and we get: h = [B]4[/B]

Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 58 dollars to rent a bike. How many hours did she pay to have the bike checked out ? Set up the cost function C(h) where h is the number of hours you rent the bike: C(h) = Hourly rental cost * h + initial rental charge C(h) = 6h + 16 Now the problem asks for h when C(h) = 58, so we set C(h) = 58: 6h + 16 = 58 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=6h%2B16%3D58&pl=Solve']type it in our math engine[/URL] and we get: h = [B]7 hours[/B]

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers? Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]x = y + 15 [*]x + y = 51 [/LIST] Plug (1) into (2) (y + 15) + y = 51 Combine like terms: 2y + 15 = 51 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get: [B]y = 18[/B] Now plug this into (1) to get: x = 18 + 15 [B]x = 33[/B]

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone. Let m be the number of months. Our equation is: [B]40m + 75 = 500 [/B] <-- This is the equation [URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get: m = [B]10.625[/B] Since it's complete months, it would be 10 months.

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages. Let r be Richard's age. And a be Alvin's age. We have: [LIST=1] [*]r = 3a [*]a + r = 52 [/LIST] Substitute (1) into (2) a + 3a = 52 Group like terms: 4a = 52 [URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B]. This means Richard is 3(13) = [B]39[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get: j = [B]24[/B]

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal? Each week, Sara's account value is: 800 - 20w <-- Subtract because Sara withdraws money each week Each week, Jordan's account value is: 500 + 30w <-- Add because Jordan deposits money each week Set them equal to each other: 800 - 20w = 500 + 30w Using our [URL='http://www.mathcelebrity.com/1unk.php?num=800-20w%3D500%2B30w&pl=Solve']equation solver[/URL], we get w = 6. Check our work: 800 - 20(6) 800 - 120 680 500 + 30(6) 500 + 180 680

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]18.09[/B]

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even. Profit per book is: P = 15 - 4 P = 11 We want to know the number of books (b) such that: 11b = 5500 <-- Breakeven means cost equals revenue [URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get: b = [B]500[/B]

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number. Let the big number be b. Let the small number be s. We're given two equations: [LIST=1] [*]b = s + 5 [*]2s + 2b = 50 [/LIST] Substitute equation (1) into equation (2) 2s + 2(s + 5) = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2B2%28s%2B5%29%3D50&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 10[/B] Now substitute s = 10 into equation (1) to solve for b: b = 10 + 5 [B]b = 15[/B]

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip? Set up the inequality where s is the number of students: C(s) = 220 + 7s We want C(s) <= 500, since at most means no more than 220 + 7s <= 500 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=220%2B7s%3C%3D500&pl=Solve']inequality calculator[/URL], we get: [B]s <= 40[/B]

The difference between two positive numbers is 5 and the square of their sum is 169. Let the two positive numbers be a and b. We have the following equations: [LIST=1] [*]a - b = 5 [*](a + b)^2 = 169 [*]Rearrange (1) by adding b to each side. We have a = b + 5 [/LIST] Now substitute (3) into (2): (b + 5 + b)^2 = 169 (2b + 5)^2 = 169 [URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get: 4b^2 + 20b + 25 Set this equal to 169 above: 4b^2 + 20b + 25 = 169 [URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get: b = (-9, 4) But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions. Substitute b = 4 into equation (1) above, and we get: a - [I]b[/I] = 5 [URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL] [B]a = 9 [/B] Therefore, we have [B](a, b) = (9, 4)[/B]

The difference of 100 and x means we subtract x from 100: 100 - x Is means equal to, so we set our expression above equal to 57 [B]100 - x = 57 [/B] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width is increased by x cm, its area is increased by 35 sq. cm. a. Express the new length and the new width in terms of x. b. Express the new area of the rectangle in terms of x. c. Find the value of x. Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get: A = 540 a) Decrease length by x and increase width by x, and we get: [LIST] [*]length = [B]30 - x[/B] [*]width = [B]18 + x[/B] [/LIST] b) Our new area using the lw = A formula is: (30 - x)(18 + x) = 540 + 35 Multiplying through and simplifying, we get: 540 - 18x + 30x - x^2 = 575 [B]-x^2 + 12x + 540 = 575[/B] c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get: [B]x = 5 or x = 7[/B] Trying x = 5, we get: A = (30 - 5)(18 + 5) A = 25 * 23 A = 575 Now let's try x = 7: A = (30 - 7)(18 + 7) A = 23 * 25 A = 575 They both check out. So we can have

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 minimum daily requirement of vitamin C for 14 year olds is at least 50 milligrams per day. An average sized apple contains 6 milligrams of vitamin C. How many apples would a person have to eat each day to satisfy this requirement? Let a be the number of apples required. The phrase [I]at least[/I] means greater than or equal to, so we have the inequality: 6a >= 50 To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6a%3E%3D50&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get: [B]a >= 8.3333 apples or rounded up to a full number, we get 9 apples[/B]

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio? Perimeter of a rectangle is: P = 2l + 2w We're given l = w + 3 and P = 54. So plug this into our perimeter formula: 54= 2(w + 3) + 2w 54 = 2w + 6 + 2w Combine like terms: 4w + 6 = 54 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 12[/B] Plug this into our l = w + 3 formula: l = 12 + 3 [B]l = 15[/B]

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: [LIST=1] [*]x + y = 5 [*]5y + 4x = 37 [/LIST] We can solve this 3 ways, using the following methods: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [B]x = -12 y = 17 [/B] Let's check our work using equation 1: -12 + 17 ? 5 5 = 5 <-- Check Let's check our work using equation 2: 5(17) + 4(-12) ? 37 85 - 48 ? 37 37 = 37 <-- Check

the sum of 23 and victor age is 59 Let's Victor's age be a. The sum of 23 and Victor's age (a) mean we add a to 23: 23 + a The word [I]is[/I] means an equation, so we set 23 + a equal to 59: [B]23 + a = 59[/B] <-- This is our algebraic expression Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get: [B]a = 36[/B]

The sum of 9 and victors age is 55 Let v be Victor's age. We have the algebraic expression: [B]v + 9 = 55 [/B] If you want to solve or v, use our [URL='http://www.mathcelebrity.com/1unk.php?num=v%2B9%3D55&pl=Solve']equation calculator[/URL].

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? [U]Givens[/U] [LIST] [*]Let Mr. Adam's age be a [*]Let Mrs. Benson's age be b [*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract: [/LIST] [LIST=1] [*]a + b = 55 [*]a - b = 3 [/LIST] Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2: (a + a) + (b - b) = 55 + 3 Combining like terms and simplifying, we get: 2a = 58 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get: a = [B]29 [/B] If a = 29, then we plug this into equation (1) to get: 29 + b = 55 b = 55 - 29 b = [B]26 [MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]

The sum of six times a number and 1 is equal to five times the number. Find the number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 6 times a number is written as: 6x the sum of six times a number and 1 is written as: 6x + 1 Five times the number is written as: 5x The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x: 6x + 1 = 5x [URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get: x = [B]-1[/B]

Two numbers that total 44 and have a difference of 6. Let the two numbers be x and y. We're given the following equations: [LIST=1] [*]x + y = 44 <-- Total means a sum [*]x - y = 6 [/LIST] Add the two equations together: (x + x) + (y - y) = 44 + 6 Cancelling the y terms, we have: 2x = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]x = 25 [/B] Rearranging equation (2) above, we get: y = x - 6 Substituting x = 25 into this, we get: y = 25 - 6 [B]y = 19[/B]

two pages that face each other in a book have a sum of 569 Pages that face each other are consecutive. Let the first page be p. The second page is p + 1. Their sum is: p + p + 1 = 569 [URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get: p = 284 This means p + 1 = 284 + 1 = 285 So the pages that face each other having a sum of 569 are: [B]284, 285[/B]

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese’s sister must be to ride? Let h be the required additional height. The phrase [I]at least[/I] means an inequality, using the >= sign, so we have: h + 41 >= 52 If we want another way to express this, we [URL='https://www.mathcelebrity.com/1unk.php?num=h%2B41%3E%3D52&pl=Solve']type this inequality into our math engine[/URL] and we get: [B]h >= 11[/B]

x tripled less two is 5 x tripled means we multiply x by 3 3x Less two means we subtract 2 from 3x 3x - 2 [I]Is[/I] means equal to, so we set 3x - 2 equal to 5 [B]3x - 2 = 5[/B] [B][/B] To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-2%3D5&pl=Solve']equation solver[/URL].

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality. Let j be the number of jeans. Let s be the number of shirts. We are given: [LIST] [*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over [/LIST] Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B]. We want to find the s that makes this inequality true. [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.

Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the washer. Company A costs $20 for the visit and $15 for every hour the person is there to fix the problem. Company B costs $40 for the visit and $5 for every hour the person is there to fix the problem. When would Company B be cheaper than Company A? Set up the cost functions: [LIST] [*]Company A: C(h) = 15h + 20 [*]Company B: C(h) = 5h + 40 [/LIST] Set them equal to each other: 15h + 20 = 5h + 40 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=15h%2B20%3D5h%2B40&pl=Solve']equation solver[/URL], we get h = 2. With [B]h = 3[/B] and beyond, Company B becomes cheaper than Company A.