Question

4) The school that Kayla goes to is selling tickets to the annual talent show. On the first day of

ticket sales the school sold 8 adult tickets and 6 child tickets for a total of $192. The school took
in $279 on the second day by selling 9 adult tickets and 12 child tickets. What is the price each
of one adult ticket and one child ticket?

Answer 1

Senior ticket = $10

Child's ticket = $8

Explanation:

s = senior ticket

c = child's ticket

We need to write 2 equations, and we have 2 unknowns, s and c.

• 3s + 5c = $70
• 12s + 12c = $216
• First solve for s using the first equation.
• 3s + 5c = 70 Subtract 5c from each side
• 3s + 5c - 5c = 70 - 5c
• 3s = 70 - 5c Divide each side by 3
• 3s/3 = (70 - 5c)/3
• s = 70-5c/3

12s + 12c = 216

12() + 12c = 216

(70 - 5c) + 12c = 216

4 (70 - 5c) + 12c = 216

280 - 20c + 12c = 216

280 - 8c = 216 Add 8c to each side

280 - 8c + 8c = 216 + 8c

280 = 216 + 8c Subtract 216 from each side.

280 - 216 = 216 - 216 + 8c

280 - 216 = 8c

64 = 8c Divide each side by 8

64/8 = 8c/8

64/8 = c

8 = c

Now plug c into the first equation and solve for s.

3s + 5c = 70

3s + 5(8) = 70

3s + 40 = 70 Subtract 40 from each side.

3s + 40 - 40 = 70 - 40

3s = 70 - 40

3s = 30 Divide each side by 3

3s/3 = 30/3

s = 30/3

s = 10

So a senior ticket costs $10 and a child's ticket costs $8.