Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Find the price of each ticket.(1 point)

Question

Responses

an adult ticket is $11 and a child ticket is $8
an adult ticket is $11 and a child ticket is $8

an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5

an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11

an adult ticket is $12.50 and a child ticket is $9.50

Answer 1

Let's define the cost of an adult ticket as \( A \) and the cost of a child ticket as \( C \).

According to the problem:

1. Three adult and three child tickets were purchased for a total of $75: \[ 3A + 3C = 75 \]

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

Now we can substitute \( C \) in the first equation:

\[ 3A + 3(A - 3) = 75 \]

Simplify the equation: \[ 3A + 3A - 9 = 75 \] \[ 6A - 9 = 75 \] \[ 6A = 75 + 9 \] \[ 6A = 84 \] \[ A = 14 \]

Now we can find the cost of a child ticket using the relation \( C = A - 3 \): \[ C = 14 - 3 = 11 \]

Thus, the ticket prices are:

• Adult ticket: $14
• Child ticket: $11

The correct response is: an adult ticket is $14 and a child ticket is $11.