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

Answer: If Shawn and Dorian each rented bikes for the same number of hours and paid the same price, their rental costs would be equal. So, we can set the two equations equal to each other and solve for x.

Shop Shawn's equation: y = 10 + 3.5x

Shop Dorian's equation: y = 6x

Setting the two equations equal to each other:

10 + 3.5x = 6x

Now, let's solve for x:

10 = 6x - 3.5x

10 = 2.5x

Divide both sides by 2.5:

x = 10 / 2.5

x = 4

So, Shawn and Dorian each rented bikes for 4 hours. Now, let's find the cost (y) for each of them:

Shop Shawn's cost (y) = 10 + 3.5x = 10 + 3.5 * 4 = 10 + 14 = 24 dollars

Shop Dorian's cost (y) = 6x = 6 * 4 = 24 dollars

Both Shawn and Dorian paid $24 for renting the bikes.