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3 adults and 2 children purchase movie tickets totalling $32.25. What were the costs for adult and children tickets?

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2 Answers

A = cost per adult ticket

C = cost per child ticket

2A + 3C = 27.75 ......(1)

3A + 2C = 32.75 ......(2)

(1)-(2): -A + C = -5
 ==>C = A-5

2A + 3C = 2A + 3(A-5) = 27.75

A = $8.55

C = A-5 = $3.55

Answer: The cost per adult ticket is $8.55, and the cost per child ticket is $3.55.

 

Comments

Sorry, this answer is wrong.  You clearly know what you're doing, but the mistake is in the original setup of equation (2):  The cost for 3 adults and 2 children is $32.25. not $32.75.  Ralph L's answer is correct.

let A be the cost of adult tickets

let C be the cost of children tickets

2A + 3C = 27.75    eq. 1

3A + 2C = 32.25    eq. 2

multiply eq.1 by -3 and multiply eq. 2 by 2:

-6A - 9C = -83.25    eq. 3

6A + 4C = 64.50     eq. 4

add eq. 3 and eq. 4:

-5C = -18.75

C = $3.75

plug in value of C into eq. 1 to get A:

2A + 3 * (3.75) = 27.75

2A + 11.25 = 27.75

2A = 27.75 - 11.25

2A = 16.50

A = $8.25

so, A = $8.25 and C = $3.75