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) Responses an adult ticket is $11 and a child ticket is $8 an adult ticket is $14 and a child ticket is $11 an adult ticket is $8 and a child ticket is $5 an adult ticket is $12.50 and a child ticket is $9.50
Let's assume the cost of an adult ticket is x dollars.
According to the given information, the cost of a child ticket is $3 less than an adult ticket, so it would be (x - 3) dollars.
The total cost of three adult tickets would be 3x dollars, and the total cost of three child tickets would be 3(x - 3) dollars.
Since the total cost of all six tickets is $75, we can set up the following equation:
3x + 3(x - 3) = 75
Simplifying the equation:
3x + 3x - 9 = 75
6x - 9 = 75
6x = 75 + 9
6x = 84
x = 84/6
x ≈ 14
So, the cost of an adult ticket is approximately $14.
Substituting this value back into the expression for the cost of a child ticket:
x - 3 ≈ 14 - 3
≈ 11
The cost of a child ticket is approximately $11.
Therefore, an adult ticket is $14 and a child ticket is $11.
So, the correct answer is: An adult ticket is $14 and a child ticket is $11.