Question

The Jones family went to a play and paid $74 for 2 adults and 2 children. The Tucker family went to the same play and paid $86 for 2 adults and 3 children. Enter the price of an adult ticket.

Answer 1

Let the price of an adult ticket be \( x \) and the price of a child ticket be \( y \).

From the information provided, we can set up the following equations based on the ticket purchases:

1. For the Jones family:
\[
2x + 2y = 74
\]

2. For the Tucker family:
\[
2x + 3y = 86
\]

Now, we can simplify the first equation:

\[
x + y = 37 \quad \text{(dividing the first equation by 2)}
\]

Now we have:

\[
(1) \quad x + y = 37
\]
\[
(2) \quad 2x + 3y = 86
\]

Next, we can solve equation (1) for \( y \):

\[
y = 37 - x
\]

Now, we can substitute \( y \) in equation (2):

\[
2x + 3(37 - x) = 86
\]

Expanding this gives:

\[
2x + 111 - 3x = 86
\]

Combining like terms results in:

\[
-x + 111 = 86
\]

Now, solve for \( x \):

\[
-x = 86 - 111
\]
\[
-x = -25
\]
\[
x = 25
\]

Now that we have the price of an adult ticket, we can find the price of a child ticket using equation (1):

\[
y = 37 - x = 37 - 25 = 12
\]

So, the price of an adult ticket is \(\boxed{25}\).