Question

Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas.
Which equation can you use to find p, the price of each movie ticket?
What was the price of each movie ticket?
$

Answer 1

Let \( p \) be the price of each movie ticket.

For Ezra:
- He bought 5 tickets, which costs \( 5p \).
- He spent $12 on popcorn.
- Total spending for Ezra is:
\[
5p + 12
\]

For Leah:
- She bought 3 tickets, which costs \( 3p \).
- She spent $24 on popcorn and $9 on sodas.
- Total spending for Leah is:
\[
3p + 24 + 9 = 3p + 33
\]

Since they spent the same amount of money, we can set their total expenditures equal to each other:
\[
5p + 12 = 3p + 33
\]

Now, we can solve for \( p \):
1. Subtract \( 3p \) from both sides:
\[
5p - 3p + 12 = 33
\]
which simplifies to:
\[
2p + 12 = 33
\]

2. Next, subtract 12 from both sides:
\[
2p = 33 - 12
\]
\[
2p = 21
\]

3. Finally, divide by 2:
\[
p = \frac{21}{2} = 10.5
\]

Thus, the price of each movie ticket is:
\[
\boxed{10.50}
\]