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

A family of 5 (2 adults & 3 children) go to the movies and they pay \$27.75. The group of 5 behind them (3 adults & 2 children) pay 32.25. Figure the cost per adult and per child. Show your work.

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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