Question

Three adult and three child move tickets were purchased for $75.00. The cost of each child ticket is $3.00 an adult ticket. Find the price of each ticket.

Answer 1

Let's define the variables for the ticket prices:

- Let the price of one adult ticket be \( A \).
- Let the price of one child ticket be \( C \).

From the problem, we know the following:

1. The total cost of three adult tickets and three child tickets is $75.00:
\[
3A + 3C = 75
\]

2. The cost of each child ticket is $3.00 less than an adult ticket:
\[
C = A - 3
\]

Now we can use these equations to solve for \( A \) and \( C \).

First, we can simplify the first equation:
\[
3A + 3C = 75 \implies A + C = 25 \quad \text{(divide everything by 3)}
\]

Now we have a new system of equations:
1. \( A + C = 25 \)
2. \( C = A - 3 \)

Next, substitute the expression for \( C \) from the second equation into the first equation:
\[
A + (A - 3) = 25
\]
This simplifies to:
\[
2A - 3 = 25
\]
Now, add 3 to both sides:
\[
2A = 28
\]
Divide by 2:
\[
A = 14
\]

Now that we know the price of an adult ticket, we can find the price of a child ticket:
\[
C = A - 3 = 14 - 3 = 11
\]

So the price of each ticket is:
- Adult ticket: \( A = 14 \) dollars
- Child ticket: \( C = 11 \) dollars

Finally, let's summarize:
- The price of an adult ticket is **$14.00**.
- The price of a child ticket is **$11.00**.