Find the price of an adult ticket and the price of a child ticket.

Question

Julia's school is selling tickets to a play. On the first day of ticket sales, the school sold 2 adult tickets and 12 child tickets for a total of $94. The school took in $73 on the second day by selling 9 adult tickets and 4 child tickets.

Answer 1

Let x = the price of an adult ticket

Let y = the price of an child ticket

2x + 12y = 94

9x + 4y = 73       Multiply this equation by -3 and add it to the first equation.

 

 2x + 12y = 94

-27x -12y = -219

-25x = -125

x = 5 adult tickets

2(5) + 12y = 94

10 + 12y = 94

12y = 84

y = 7 child tickets

 

Answer 2

a = price of adult

c = price of child

 

2a + 12c = 94

9a + 4c = 73

 

Solve simultaneously for a and c by substitution, matrix methods, or Cramer's rule, and get

 

a = $5

c = $7

 

I am surprised that the adult price is lower, but that is what the numbers give, for the problem as stated.  (Could the numbers for adult and children be stated backwards in the problem?) Test the answers.