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? round to the nearest dollar if necessary.
\bigcirc 3
\bigcirc 4
\bigcirc 14
\bigcirc 24

Explanation:

Step1: Set the two equations equal

Since they paid the same price, set \(10 + 3.5x=6x\)

Step2: Solve for x

Subtract \(3.5x\) from both sides: \(10 = 6x - 3.5x\)
Simplify: \(10 = 2.5x\)
Divide both sides by 2.5: \(x=\frac{10}{2.5}=4\)

Step3: Find the price

Use \(y = 6x\) (or \(y=10 + 3.5x\)) with \(x = 4\)
\(y=6\times4 = 24\) (or \(y=10+3.5\times4=10 + 14 = 24\))

Answer:

24 (corresponding to the option: 24)