Johnny is selling tickets to a school play. On the first day of ticket sales he sold 14 senior citizen tickets and 4 child tickets for a total of $200. On the second day of ticket sales he sold 7 senior citizen tickets and 1 child ticket for a total of $92. What is the price of one child ticket?

Johnny is selling tickets to a school play. On the first day of ticket sales he sold 14 senior (S) citizen tickets and 4 child (C) tickets for a total of $200. On the second day of ticket sales he sold 7 senior (S) citizen tickets and 1 child (C) ticket for a total of $92. What is the price of one child ticket?

14S + 4C = 200

14S = 200 - 4C

S = (200 - 4C) / 14

7S + 1C = 92

7S = 92 - C

S = (92 - C) / 7

(200 - 4C) / 14 = (92 - C) / 7

7 x (200 - 4C) = 14 x (92 - C)

1400 - 28C = 1288 - 14C

1400 - 1288 = 28C - 14C

112 = 14C

C = 112/14 = 8

the price of one child ticket = $8