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? $

Explanation:

Step1: Set the two equations equal

Since they paid the same price and rented for the same hours, set \(10 + 3.5x=6x\).

Step2: Solve for x

Subtract \(3.5x\) from both sides: \(10 = 6x - 3.5x\), which simplifies to \(10 = 2.5x\). Then divide both sides by \(2.5\): \(x=\frac{10}{2.5}=4\).

Step3: Find the price

Substitute \(x = 4\) into one of the equations, say \(y = 6x\). Then \(y=6\times4 = 24\).

Answer:

24