Question

A baseball coach brings her team to a fun center to practice batting. There are 2 fun centers in the town. Players at each fun center buy tokens to use at the batting cages. Each token will give the player 15 pitches.
• The equation y = 2x represents the cost, y, in dollars to buy x tokens at Center A.
• The equation y = 2. 5x represents the cost, y, in dollars to buy x tokens at Center B.
The coach takes her team to Center A and buys tokens that will give the team 150 pitches.
How many pitches could the team get at Center B for the same amount the coach spent at Center A? Enter the answer in the box.

Answer 1

First, we need to determine how many tokens the coach buys at Center A to get 150 pitches. Each token provides 15 pitches, so we can calculate the number of tokens needed:

\[
\text{Number of tokens} = \frac{\text{Total pitches}}{\text{Pitches per token}} = \frac{150}{15} = 10 \text{ tokens}
\]

Now, using the equation for the cost at Center A:

\[
y = 2x
\]

we can find out the total cost for 10 tokens:

\[
y = 2(10) = 20 \text{ dollars}
\]

Next, we need to find out how many pitches the team could get at Center B for the same amount spent, which is $20. The cost equation for Center B is:

\[
y = 2.5x
\]

We need to solve for \(x\) (the number of tokens) when \(y = 20\):

\[
20 = 2.5x
\]

To solve for \(x\):

\[
x = \frac{20}{2.5} = 8 \text{ tokens}
\]

Now, we can find out how many pitches these 8 tokens represent at Center B:

\[
\text{Total pitches} = 8 \text{ tokens} \times 15 \text{ pitches per token} = 120 \text{ pitches}
\]

Therefore, the team could get **120 pitches** at Center B for the same amount the coach spent at Center A.