Question

At the skating rink, David paid $ 20 and skated for 3 hours while Jennifer skated for 2 hours and paid $ 15. Both of the prices include the price of renting skates.

the cost per hour is $___
the inital skate rental cost is $ ____

Answer 1

Let's denote the cost per hour of skating as \( x \) and the initial skate rental cost as \( y \).

From the information given, we can set up the following equations based on David's and Jennifer's costs:

1. For David:
\[
3x + y = 20 \quad \text{(1)}
\]

2. For Jennifer:
\[
2x + y = 15 \quad \text{(2)}
\]

Now, we can solve these equations simultaneously.

First, we can eliminate \( y \) by subtracting equation (2) from equation (1):

\[
(3x + y) - (2x + y) = 20 - 15
\]
This simplifies to:
\[
x = 5
\]

Now that we have the cost per hour, we can substitute \( x = 5 \) back into one of the original equations to find \( y \). Let's substitute into equation (2):

\[
2(5) + y = 15
\]

This simplifies to:
\[
10 + y = 15
\]
Thus,
\[
y = 15 - 10 = 5
\]

Now we have both values:
- The cost per hour is \( x = 5 \).
- The initial skate rental cost is \( y = 5 \).

So, the answers are:
- The cost per hour is **$5**.
- The initial skate rental cost is **$5**.