Question

My school that's even Rose to is selling tickets to a charcoal performance in the first day of the ticket sale the school sold three senior citizen tickets and while one child ticket for total $38 the school took and $52 in the second day by selling three senior services tickets and two child tickets find the price of a senior citizen ticket and the price of a child ticket

Answer 1

Let's denote the price of a senior citizen ticket as \( S \) and the price of a child ticket as \( C \). We can set up a system of equations based on the information provided.

From the first day of ticket sales, we know:
- 3 senior citizen tickets and 1 child ticket were sold for a total of $38.
This gives us our first equation:
\[
3S + C = 38 \quad \text{(1)}
\]

From the second day of sales, we know:
- 3 senior citizen tickets and 2 child tickets were sold for a total of $52.
This gives us our second equation:
\[
3S + 2C = 52 \quad \text{(2)}
\]

Now we can solve this system of equations. We can start by solving equation (1) for \( C \):
\[
C = 38 - 3S \quad \text{(3)}
\]

Next, we can substitute equation (3) into equation (2):
\[
3S + 2(38 - 3S) = 52
\]

Now expand and simplify:
\[
3S + 76 - 6S = 52
\]
\[
-3S + 76 = 52
\]
\[
-3S = 52 - 76
\]
\[
-3S = -24
\]
\[
S = 8
\]

Now that we have \( S \), we can substitute it back into equation (3) to find \( C \):
\[
C = 38 - 3(8)
\]
\[
C = 38 - 24
\]
\[
C = 14
\]

Thus, the price of a senior citizen ticket is **$8**, and the price of a child ticket is **$14**.