Let's denote the cost of an adult ticket as \( x \) dollars. Since the cost of each child ticket is $3 less than the cost of an adult ticket, the cost of a child ticket would be \( x - 3 \) dollars.
According to the problem, three adult tickets and three child tickets were purchased for a total of $75. We can set up the following equation:
\[ 3x + 3(x - 3) = 75 \]
Now, let's simplify and solve for \( x \):
-
Distribute the 3 in the second term: \[ 3x + 3x - 9 = 75 \]
-
Combine like terms: \[ 6x - 9 = 75 \]
-
Add 9 to both sides: \[ 6x = 84 \]
-
Divide by 6: \[ x = 14 \]
Now that we have the cost of the adult ticket, we can find the cost of the child ticket: \[ x - 3 = 14 - 3 = 11 \]
Finally, the prices of the tickets are:
- Adult ticket: $14
- Child ticket: $11
So, the answer is:
- Adult ticket: $14
- Child ticket: $11
8 answers