Adult tickets for the school play sold for $3.50 and student tickets sold for $2.50. Three hundred twenty-one tickets were sold altogether for $937.50. How many of each kind of ticket were sold?

Question

Genesis Allen · Accepted Answer

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Eva Abramson · Answer

undefined Let x be the number of adult tickets sold and y be the number of student tickets sold. The total revenue from adult tickets is 3.50x, and the total revenue from student tickets is 2.50y. 
The total number of tickets sold is x + y = 321.
The total revenue from all tickets sold is 3.50x + 2.50y = 937.50.
Solving the system of equations:
x + y = 321
3.50x + 2.50y = 937.50
We can solve for x and y:
x = 237
y = 84
Therefore, 237 adult tickets and 84 student tickets were sold.

HIX Tutor · Answer

undefined Let's find out how many adult and student tickets were sold.

1. **Set up the problem:**
   - Let $ A $ be the number of adult tickets.
   - Let $ S $ be the number of student tickets.

2. **Write equations:**
   - Total tickets sold: $ A + S = 321 $ (Equation 1)
   - Total money made: $ 3.50A + 2.50S = 937.50 $ (Equation 2)

3. **Solve Equation 1 for $ S $:**
   - $ S = 321 - A $

4. **Substitute $ S $ in Equation 2:**
   - $ 3.50A + 2.50(321 - A) = 937.50 $

5. **Distribute $ 2.50 $:**
   - $ 3.50A + 802.50 - 2.50A = 937.50 $

6. **Combine like terms:**
   - $ (3.50A - 2.50A) + 802.50 = 937.50 $
   - $ 1.00A + 802.50 = 937.50 $

7. **Subtract $ 802.50 $ from both sides:**
   - $ 1.00A = 937.50 - 802.50 $
   - $ 1.00A = 135 $

8. **So, $ A = 135 $** adult tickets.

9. **Now find $ S $:**
   - Using $ S = 321 - A $
   - $ S = 321 - 135 $
   - $ S = 186 $ student tickets.

10. **Final Answer:**
   - Adult tickets sold: **135**
   - Student tickets sold: **186**