Question

Pls solve correctly.
At a concert, adult tickets cost $30 each, and child ticket costs $15 each. If the total revenue from selling 200 tickets was $4200. How many adults and child tickets were sold?

Answer 1

Let \( x \) be the number of adult tickets sold and \( y \) be the number of child tickets sold.

We have the following two equations based on the information given:

1. The total number of tickets sold:
\[
x + y = 200
\]

2. The total revenue from ticket sales:
\[
30x + 15y = 4200
\]

Now, we can solve this system of equations.

First, we can simplify the second equation by dividing everything by 15:
\[
2x + y = 280
\]

Now, we have the system of equations:
1. \( x + y = 200 \)
2. \( 2x + y = 280 \)

Next, we can subtract the first equation from the second equation:
\[
(2x + y) - (x + y) = 280 - 200
\]
This simplifies to:
\[
x = 80
\]

Now that we have \( x \), we can find \( y \) using the first equation:
\[
80 + y = 200
\]
\[
y = 200 - 80 = 120
\]

Thus, the number of adult tickets sold is \( 80 \) and the number of child tickets sold is \( 120 \).

In summary:
- Adult tickets sold: \( 80 \)
- Child tickets sold: \( 120 \)