Question

Sylvester and Lin go to the amusement park. Sylvester plays 5 rounds of mini golf and takes 4 turns in the batting cages for $60. Lin plays 3 rounds of mini golf and takes 6 turns in the batting cages for $45. Use two equations to find the price for each activity. Enter your answers in the boxes.

Mini golf costs $
per round and batting cages cost $
each turn.

Answer 1

Let \( x \) be the price per round of mini golf and \( y \) be the price per turn in the batting cages. We can set up the following equations based on the information provided:

1. For Sylvester:
\[
5x + 4y = 60
\]

2. For Lin:
\[
3x + 6y = 45
\]

Now, let's solve this system of equations.

We can start with the first equation:

\[
5x + 4y = 60
\]

We can express \( y \) in terms of \( x \):

\[
4y = 60 - 5x
\]
\[
y = \frac{60 - 5x}{4}
\]

Next, substitute this expression for \( y \) into the second equation:

\[
3x + 6\left(\frac{60 - 5x}{4}\right) = 45
\]

To eliminate the fraction, we can multiply the entire equation by 4:

\[
12x + 6(60 - 5x) = 180
\]

Distributing \( 6 \):

\[
12x + 360 - 30x = 180
\]

Combine like terms:

\[
-18x + 360 = 180
\]

Subtract 360 from both sides:

\[
-18x = 180 - 360
\]
\[
-18x = -180
\]

Dividing both sides by -18:

\[
x = 10
\]

Now substitute \( x = 10 \) back into the equation for \( y \):

\[
y = \frac{60 - 5(10)}{4}
\]
\[
y = \frac{60 - 50}{4}
\]
\[
y = \frac{10}{4} = 2.5
\]

Thus, the prices are:
- Mini golf costs \( \mathbf{10} \) dollars per round,
- Batting cages cost \( \mathbf{2.5} \) dollars per turn.

Final answers:
- Mini golf costs $10 per round.
- Batting cages cost $2.50 each turn.