SOLUTION: Lydia and her friends want to rent a boat, so they start shopping around. Store ABC charges an initial fee of $50, plus $10 for every hour of rental. Store XYZ charges an initia

Algebra ->  Average -> SOLUTION: Lydia and her friends want to rent a boat, so they start shopping around. Store ABC charges an initial fee of $50, plus $10 for every hour of rental. Store XYZ charges an initia      Log On


   

Question 1135026: Lydia and her friends want to rent a boat, so they start shopping around. Store ABC charges an initial fee of $50, plus $10 for every hour of rental. Store XYZ charges an initial fee of $40, plus $15 for every hour of rental. At what
number of hour renting a boat from either store be same?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula to use is y = m * x + b.

b is the initial charger.
m is the hourly charge.
x is the number of hours.
y is the total cost.

store ABC charges an initial fee of 50 dollars plus 10 dollars for every hour of rental.

the formula for ABC is y1 = 10 * x + 50

store XYZ charges an initial fee of 40 dollars plus 15 dollars for every hour of rental.

the formula for XYZ is y2 = 15 * x + 40

when the total is the same, y1 is equal to y2.

since y1 is equal to 10 * x + 50 and y2 is equal to 25 * x + 40, you get:

10 * x + 50 = 15 * x + 40

subtract 40 from both sides of this equation and subtract 10 * x from both sides of this equation to get:

50 - 40 = 15 * x - 10 * x

simplify to get 10 = 5 * x

solve for x to get x = 2

if you rent the boat for 2 hours, the cost would be the same whether you used ABC or XYZ

when x = 2, ABC cost is 50 + 10 * 2 = 70.

when x = 2, XYZ cost is 40 + 2 * 15 = 70.

your solution is 2 hours.