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.
$
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Answer 1

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

According to the information provided:

1. The Jones family paid $74 for 2 adults and 2 children:
\[
2a + 2c = 74
\]

2. The Tucker family paid $86 for 2 adults and 3 children:
\[
2a + 3c = 86
\]

Now we have a system of equations:
1. \( 2a + 2c = 74 \) \quad (1)
2. \( 2a + 3c = 86 \) \quad (2)

We can solve this system step by step. First, let's simplify equation (1) by dividing everything by 2:
\[
a + c = 37 \quad (3)
\]

Now we will subtract equation (1) from equation (2):
\[
(2a + 3c) - (2a + 2c) = 86 - 74
\]
This simplifies to:
\[
c = 12
\]

Now that we have the value for \( c \), we can substitute it back into equation (3) to find \( a \):
\[
a + 12 = 37
\]
\[
a = 37 - 12
\]
\[
a = 25
\]

Therefore, the price of an adult ticket is:
\[
\boxed{25}
\]