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

To find out how much Shawn and Dorian each paid for the rental, we start with the equations representing their bike rental costs:

For Shawn:
\[
y = 10 + 3.5x
\]

For Dorian:
\[
y = 6x
\]

Since they paid the same price, we can set the equations equal to each other:

\[
10 + 3.5x = 6x
\]

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

First, let's isolate \(x\) terms on one side:

\[
10 = 6x - 3.5x
\]

This simplifies to:

\[
10 = 2.5x
\]

Next, we divide both sides by 2.5 to find \(x\):

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

Now that we have \(x = 4\) (the number of hours they rented the bikes), we can substitute \(x\) back into either equation to find the rental price. We will use Dorian's equation for this:

\[
y = 6x = 6(4) = 24
\]

We will also confirm using Shawn's equation:

\[
y = 10 + 3.5(4) = 10 + 14 = 24
\]

Both formulas confirm that they each paid \(y = 24\) dollars.

Thus, the amount each paid for the rental is:

\[
\boxed{24}
\]