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.

3
4
14
24

Answer 1

To find how much Shawn and Dorian paid for the rental, we need to set their renting prices equal to each other, since they paid the same price for the same number of hours.

The equations for the two shops are:
- Shawn's rental cost: \( y = 10 + 3.5x \)
- Dorian's rental cost: \( y = 6x \)

Setting them equal to each other:

\[
10 + 3.5x = 6x
\]

Now, we can solve for \( x \):

1. Subtract \( 3.5x \) from both sides:

\[
10 = 6x - 3.5x
\]

2. Simplify:

\[
10 = 2.5x
\]

3. Divide by \( 2.5 \):

\[
x = \frac{10}{2.5} = 4
\]

Now that we have found \( x \), which is 4 hours, we can plug this value back into either of the rental equations to find the price.

Using Dorian's equation:

\[
y = 6x = 6 \times 4 = 24
\]

Alternatively, using Shawn's equation:

\[
y = 10 + 3.5 \times 4 = 10 + 14 = 24
\]

Thus, both Shawn and Dorian paid the same amount for the bike rental, which is **$24**.