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

Let the number of adult tickets sold be $ x $ and the number of student tickets sold be $ y $.

We have two pieces of information:

1. The total number of tickets sold was 375:
   \[
   x + y = 375
   \]
   
2. The total amount collected from the ticket sales was $2,212.50. The adult tickets were sold for $7.50 each, and the student tickets were sold for $4.50 each:
   \[
   7.50x + 4.50y = 2212.50
   \]

### Step 1: Solve for $ x $ in terms of $ y $
From the first equation, solve for $ x $:
\[
x = 375 - y
\]

### Step 2: Substitute $ x $ into the second equation
Substitute $ x = 375 - y $ into the second equation:
\[
7.50(375 - y) + 4.50y = 2212.50
\]

### Step 3: Simplify and solve for $ y $
First, distribute the $ 7.50 $ on the left side:
\[
7.50(375) - 7.50y + 4.50y = 2212.50
\]
\[
2812.50 - 7.50y + 4.50y = 2212.50
\]
Combine like terms:
\[
2812.50 - 3y = 2212.50
\]
Subtract 2212.50 from both sides:
\[
600 = 3y
\]
Solve for $ y $:
\[
y = \frac{600}{3} = 200
\]

### Conclusion:
The junior class sold **200 student tickets**.

Would you like more details on any step or further explanations?

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Here are 5 related questions to expand on this problem:

1. How many adult tickets were sold?
2. What would the total be if all tickets were student tickets?
3. What if the price of student tickets increased to $5.50, how would that change the sales total?
4. How much money would be made if only 300 tickets were sold, keeping the same adult-to-student ratio?
5. What percentage of the total tickets sold were student tickets?

**Tip:** When solving word problems, translating the information into clear equations is a key step!

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?

Discover how to solve a word problem involving ticket sales at Summerfield High School's spring festival. This problem uses algebra and linear equations to determine how many student tickets were sold. Perfect for students in Grades 8-10.

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