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ne drama club sold a total of 360 adult and student tickets for the school play. Charging $5 for each adult ticket and $3 for each student ticket, they ollected $1,360 from ticket sales. How many student tickets did the drama club sell?



Answer :

ynahayuri
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.

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