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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 = 9 - x Check our...

Allen saves $162 a month. Allen saves $43 less each month than Lane. How much will Lane save in 2 years? Calculate Lane's monthly savings: Lane's monthly savings = Allen's monthly savings + 43 (since Allan saves 43 less than Lane) Lane's monthly savings = 162 + 43 Lane's monthly savings = 205...

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: x = y <-- Because we have the phrase that are equal x + y = 60 Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add...

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...

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver Let d be the total number of deliveries the paper boy makes on the route. d We're given, d/7 = 13 d = 13 * 7 d = 91

If 25% of 30% of x is 9, what is x? Convert percentages to decimals when multiplying: 25% = 0.25 30% = 0.3 0.25 * 0.3 * x = 9 0.075x = 9 Using our math engine, we type this equation in and we get: x = 120

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given? 582 passengers on the boat Let r be the number of rides So we want to find r when: 582r = 13105 To solve for r...

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s +...

A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x represent the number of dimes, and let y represent the number of quarters. Since amount = cost * quantity, we have: 0.1d + 0.25q = 90.25

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 type this equation...

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...

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options? Option A payment function: 24h...

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...

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters. Let h be the number of hours. We're given the following expression for the printing output of the machine: 230h The questions asks for how long (h)...

If EF = 7x , FG = 3x , and EG = 10 , what is EF? By segment addition: EF + FG = EG 7x + 3x = 10 To solve this equation for x, we type it in our search engine and we get: x = 1 Evaluating EF = 7x with x = 1, we get: EF = 7 * 1 EF = 7

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bob gets his $1200 goal? Set up he savings function S(h) where h is the number of hours needed: S(h) = savings per hour * h + current savings amount S(h) = 20h + 400 The question asks for h when...

kyle baked 29 muffins. He placed p muffins each in 4 boxes and had 5 muffins left over. How many muffins were in each box We set up the following equation: 4p + 5 = 29 To solve this equation for p, we type it in our math engine and we get: p = 6

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in...

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 − 1800x dollars. After how many months will the value of the building be $409,200? We want to know x for the...

If FG=11, GH=x-2, and FH=3x-11, what is FH By segment addition, we have: FG + GH = FH 11 + x - 2 = 3x - 11 To solve this equation for x, we type it in or math engine and we get: x = 10 FH = 3x - 11. So we substitute x = 10 into this: FH = 3(10) - 11 FH = 30 - 11 FH = 19