Question

Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y = 10 + 3.5x Shop Dorian used: y = 6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental?

Answer 1

If you would like to know how much did each pay for the rental, you can calculate this using the following steps:

y = 10 + 3.5 * x
y = 6 * x
_____________
10 + 3.5 * x = 6 * x
10 = 6 * x - 3.5 * x
10 = 2.5 * x
x = 10 / 2.5
x = 4 hours

y = 6 * x = 6 * 4 = 24 dollars

y = 10 + 3.5 * x = 10 + 3.5 * 4 = 24 dollars

They both paid 24 dollars for 4 hours.

Answer 2

You need to find the solution to the system of equations:

y = 10 + 3.5x
y = 6x

Then, both right sides are equal to each other:

6x = 10 +3.5x

6x - 3.5x = 10

2.5x = 10

x = 10/2.5 = 4

And:

y = 6(4) = 24.

Answer: They both rented the bikes for 4 hours and paid $ 24.