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)
• 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 $14 and a child ticket is S11
• an adult ticket is $12.50 and a child ticket is $9.50
Let's denote the cost of an adult ticket as A and the cost of a child ticket as C.
From the problem, we know the following information:
- 3 adult tickets + 3 child tickets = $75
- The cost of each child ticket is $3 less than the cost of an adult ticket.
Let's set up a system of equations to solve for A and C:
Equation 1: 3A + 3C = 75
Equation 2: C = A - 3
Now, let's substitute Equation 2 into Equation 1:
3A + 3(A - 3) = 75
3A + 3A - 9 = 75
6A - 9 = 75
6A = 84
A = 14
Now, substitute the value of A into Equation 2 to solve for C:
C = 14 - 3
C = 11
Therefore, the price of each ticket is:
- an adult ticket is $14
- a child ticket is $11