Question

The junior class at Summerfield High School sold a total of 375 tickets for their spring festival. The adult tickets sold for $7.50 each and the student tickets sold for $4.50 each.

If the junior class collected $2,212.50 in ticket sales, how many student tickets did the class sell?

Answer 1

To solve this problem, we can set up a system of equations based on the information provided.

Let:
- \( x \) = number of adult tickets sold
- \( y \) = number of student tickets sold

We have the following equations based on the problem statement:

1. The total number of tickets sold:
\[
x + y = 375
\]

2. The total revenue collected from ticket sales:
\[
7.5x + 4.5y = 2212.50
\]

Now, we can solve this system of equations step by step.

First, from the first equation, express \( x \) in terms of \( y \):
\[
x = 375 - y
\]

Next, substitute this expression for \( x \) into the second equation:
\[
7.5(375 - y) + 4.5y = 2212.50
\]

Distributing \( 7.5 \):
\[
2812.5 - 7.5y + 4.5y = 2212.50
\]

Combining the \( y \) terms:
\[
2812.5 - 3y = 2212.50
\]

Subtract \( 2812.5 \) from both sides:
\[
-3y = 2212.50 - 2812.5
\]
\[
-3y = -600
\]

Now, divide both sides by \(-3\):
\[
y = 200
\]

So, the number of student tickets sold is \( \boxed{200} \).

To confirm the result, we can find \( x \):
\[
x = 375 - y = 375 - 200 = 175
\]

Now, we check the revenue:
\[
7.5x + 4.5y = 7.5(175) + 4.5(200)
\]
Calculating these:
- \( 7.5 \times 175 = 1312.5 \)
- \( 4.5 \times 200 = 900 \)

Now summing these two amounts:
\[
1312.5 + 900 = 2212.5
\]

Since the total matches the revenue provided in the problem, our solution is verified. Thus, the number of student tickets sold is indeed \( \boxed{200} \).