Solve each system below using either substitution or elimination. the final answer in (x, y) form.

Question

Dan's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 1

senior citizen ticket and 2 child tickets for a total of $37. The school took in $323 on the second

day by selling 14 senior citizen tickets and 13 child tickets. What is the price each of one senior

citizen ticket and one child ticket?

Answer 1

Let x = price of a senior ticket and y = price of a child's ticket

x + 2y = 37

14x + 13y = 323

From the first equation, x = 37-2y

Substitute for x in the other equation to get 14(37 - 2y) + 13y = 323

-15y = -195

y = 13 and x = 11

Each senior ticket costs $11 and each child's ticket costs $13.

Answer 2

11 seniors and 13 children

S+2C = 37

14S +28C = 37(14)= 518, subtract

14S+13C =323

15C =518-323= 195

C=195/15= 13 children

S =37-2(13) = 11 seniors

(S,C) = (11,13) = (x,y)