Use the information to answer the question.
Information
The cost of 4 adult tickets and 2 student tickets is $132. The cost of 2 adult tickets and 6 student tickets is $156.
Question
What is the cost of each type of ticket? Enter the answers in the boxes.
Response area with 2 text input boxes
Each adult ticket costs dollars
and each student ticket costs dollars
Let's assume that the cost of an adult ticket is "A" dollars and the cost of a student ticket is "S" dollars.
From the given information, we can create the following equations:
4A + 2S = 132 (equation 1)
2A + 6S = 156 (equation 2)
Solving these equations will help us find the values of A and S.
Multiplying equation 1 by 3 and multiplying equation 2 by 2, we have:
12A + 6S = 396 (equation 3)
4A + 12S = 312 (equation 4)
Now, subtracting equation 4 from equation 3, we get:
12A + 6S - (4A + 12S) = 396 - 312
8A - 6S = 84
8A = 6S + 84
A = (6/8)S + 10.5
A = (3/4)S + 10.5
Now, substituting the value of A in equation 1, we have:
4((3/4)S + 10.5) + 2S = 132
3S + 42 + 2S = 132
5S + 42 = 132
5S = 132 - 42
5S = 90
S = 90/5
S = 18
Now, substituting the value of S back into A = (3/4)S + 10.5, we have:
A = (3/4) * 18 + 10.5
A = (3/4) * 18 + 10.5
A = 13.5 + 10.5
A = 24
Therefore, each adult ticket costs $24 and each student ticket costs $18.