Question

A movie theater charges different prices for children and adults. On Friday, 10 adults and 25 children went to the movie and it cost $670. On Sunday 5 adults and 10 children went and it cost $290. (4 po

Answer 1

To find the prices for adults and children at the movie theater, we can set up a system of equations based on the information provided.

Let's denote:
- \( a \) as the price of an adult ticket
- \( c \) as the price of a child ticket

From the information given, we can create the following equations:

1. From Friday's ticket sales:
\[
10a + 25c = 670 \tag{1}
\]

2. From Sunday's ticket sales:
\[
5a + 10c = 290 \tag{2}
\]

We can simplify Equation (2) by dividing each term by 5:
\[
a + 2c = 58 \tag{3}
\]

Now we have a simpler equation to work with. Next, we can solve Equation (3) for \( a \):
\[
a = 58 - 2c \tag{4}
\]

Now, we will substitute Equation (4) into Equation (1):
\[
10(58 - 2c) + 25c = 670
\]
Distributing 10 gives us:
\[
580 - 20c + 25c = 670
\]
Combining like terms:
\[
580 + 5c = 670
\]
Subtracting 580 from both sides:
\[
5c = 90
\]
Dividing by 5:
\[
c = 18
\]

Now that we have \( c \) (the cost of a child ticket), we can substitute it back into Equation (4) to find \( a \):
\[
a = 58 - 2(18)
\]
Calculating this gives:
\[
a = 58 - 36 = 22
\]

Thus, the prices for the tickets are:
- Adult ticket price \( a = 22 \) dollars
- Child ticket price \( c = 18 \) dollars

### Final Answer:
- Adult ticket price: $22
- Child ticket price: $18