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

From the information given, we can set up the following two equations:

1. For the Jones family:
\[
2a + 2c = 74
\]

2. For the Tucker family:
\[
2a + 3c = 86
\]

Now, we can simplify the first equation by dividing everything by 2:
\[
a + c = 37 \quad \text{(Equation 1)}
\]

Next, we can rearrange Equation 1 to express \( c \) in terms of \( a \):
\[
c = 37 - a
\]

Now, we can substitute this expression for \( c \) into the second equation:
\[
2a + 3(37 - a) = 86
\]

Expanding this gives:
\[
2a + 111 - 3a = 86
\]

Now combine like terms:
\[
-1a + 111 = 86
\]

Subtract 111 from both sides:
\[
-1a = 86 - 111
\]
\[
-1a = -25
\]

Multiplying both sides by -1 gives:
\[
a = 25
\]

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