To find out how many student tickets the drama club sold, we can set up a system of equations based on the given information.
Let's define:
- \( x \) as the number of adult tickets sold
- \( y \) as the number of student tickets sold
From the problem, we have the following two equations:
1. The total number of tickets sold:
\[ x + y = 360 \]
2. The total amount of money collected:
\[ 5x + 3y = 1360 \]
We can solve this system of equations step by step.
First, solve the first equation for \( x \):
\[ x = 360 - y \]
Next, substitute \( x \) in the second equation:
\[ 5(360 - y) + 3y = 1360 \]
Distribute the 5:
\[ 1800 - 5y + 3y = 1360 \]
Combine like terms:
\[ 1800 - 2y = 1360 \]
Subtract 1800 from both sides:
\[ -2y = 1360 - 1800 \]
\[ -2y = -440 \]
Divide by -2:
\[ y = 220 \]
So, the number of student tickets sold is \( 220 \).
To check, substitute \( y \) back into the first equation to find \( x \):
\[ x + 220 = 360 \]
\[ x = 140 \]
Finally, verify the total amount collected:
\[ 5x + 3y = 5(140) + 3(220) = 700 + 660 = 1360 \]
The calculations are correct, so the drama club sold \( 220 \) student tickets.
