What is the price of each king of ticket?

Question

A local kids play sold 8 adult ticket and 9 child tickets for a total of $205. The next day they sold only 4 adult tickets and 3 child tickets for a total of $83.

Answer 1

X = adult ticket price

Y = child ticket price

 

8X + 9Y = 205

4X + 3Y = 83

 

Multiplies the bottom equation by -3 

   8X +  9Y =   205
-12X + -9Y = -249

 

Adding them together:

  -4X = -44

 

    X= -44/-4 = $11

   Plugging this into the second equation because the numbers are smaller...

   4(11)+ 3Y = 83

   44 + 3Y = 83

    3Y = 83 - 44

    3Y = 39

    Y = 13

 

  using the first equation to check:

 

  8X + 9Y = 8(11)+9(13) =

 

                    88 +  117 

                    = 205

 

Adult costs 11.

Child costs 13.

CHild costs more than the adult.... why?