Question

At the skating rink, David paid $
18.5
18.5 and skated for 3 hours while Jennifer skated for 2 hours and paid $
14.0
14.0. Both of the prices include the price of renting skates. Click Here for Help Video





The cost per hour is $
.

The initial skate rental cost is is $
.

Answer 1

Let's denote the skate rental cost as \( r \) and the cost per hour as \( c \).

From the problem, we can set up the following equations based on the information given:

For David:
\[
r + 3c = 18.5
\]

For Jennifer:
\[
r + 2c = 14.0
\]

Now, we can solve these two equations simultaneously.

First, let's subtract the second equation from the first:

\[
(r + 3c) - (r + 2c) = 18.5 - 14.0
\]
This simplifies to:
\[
c = 4.5
\]

Now that we have the cost per hour \( c = 4.5 \), we can substitute \( c \) back into one of the original equations to find the rental cost \( r \). Using Jennifer's equation:

\[
r + 2(4.5) = 14.0
\]

This simplifies to:
\[
r + 9 = 14.0
\]
\[
r = 14.0 - 9 = 5.0
\]

Thus, the answers are:

- The cost per hour is \( \boxed{4.5} \).
- The initial skate rental cost is \( \boxed{5.0} \).