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.

Question

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

GPT-4o mini · Answer

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:

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