Question

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold?

Answer 1

Let \( x \) be the number of student tickets sold and \( y \) be the number of adult tickets sold. We can set up the following equations based on the information given:

1. The total number of tickets sold is 530:
\[
x + y = 530
\]

2. The total receipts from ticket sales were $1740:
\[
3x + 4y = 1740
\]

Now, we can solve this system of equations. We can start with the first equation and express \( y \) in terms of \( x \):
\[
y = 530 - x
\]

Next, we substitute \( y \) into the second equation:
\[
3x + 4(530 - x) = 1740
\]

Distributing the 4 gives:
\[
3x + 2120 - 4x = 1740
\]

Now, combine like terms:
\[
-1x + 2120 = 1740
\]

Subtract 2120 from both sides:
\[
-x = 1740 - 2120
\]
\[
-x = -380
\]

Now, multiplying both sides by -1:
\[
x = 380
\]

Now that we have found \( x \), we can substitute it back into the equation for \( y \):
\[
y = 530 - x = 530 - 380 = 150
\]

Thus, the number of student tickets sold is \( x = 380 \) and the number of adult tickets sold is \( y = 150 \).

Finally, we conclude that:
- Number of student tickets sold: \( \boxed{380} \)
- Number of adult tickets sold: \( \boxed{150} \)