Question

Two families went to see the Hawks play last night. One family paid $144

for four adult tickets and 8 child tickets. The other family paid $136 for 6
adult tickets and 4 child tickets. What is the price for each adult ticket and
each child's ticket?
Price for Adult Ticket =
Price for Child Ticket =
Jury

Answer 1

• Adult: $16
• Child: $10

Explanation:

You want to know the price of each kind of ticket when 4 adult and 8 child tickets cost $144, and 6 adult and 4 child tickets cost $136.

Setup

We can use an equation to describe each of the purchases:

4a +8c = 144

6a +4c = 136

Solution

We can divide the first equation by 2 and subtract it from the second:

(6a +4c) -1/2(4a +8c) = (136) -1/2(144)

4a = 64 . . . . . . . simplify

a = 16

Using this value in the second equation gives ...

6·16 +4c = 136

4c = 40 . . . . . . . subtract 96

c = 10

The price for an adult ticket was $16; for a child ticket, $10.

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