word problem

Question

mark is selling tickets to a spring musical. on the first of ticket sales the school sold 2 adult tickets and 8 child ticket for a total of $138. The school took in $202 on the second day by selling 8 adult tickets and 7 child tickets. find the price of an adult ticket and a child ticket.

Answer 1

Two equations with 2 unknowns.

a = cost of adult tickets

c = cost of child tickets

 

2a + 8c = 138.   {equation 1}

8a + 7c = 202.   {equation 2}

 

Let's solve by elimination.  Multiply equation 1

by -4 and add equations to eliminate 'a'

 

-8a - 32c = -552

 8a + 7c =   202

------------------------

       -25c = -350

         c = $14 per child ticket

 

Plug this value into either equation 1

or equation 2 and solve for a.

Answer 2

Let A be the price of adult tickets and C the price of Child tickets.  

Theh price of 2 adult tickets and 8 child tickets, given to be $138, is then:

2A+8C =138

 

The price of 8 adult tickets and 7 child tickets, given to be $202, is then:

8A + 7C = 202

 

The first equation can be multiplied by -4 (both sides) to give:

 

-8A - 32C = -552

 

Add this to the first one.  The A's cancel:

 

C(-64+7) = -552+202

-25C = -350

C=14

 

Plug this back into the first one to give:

2A + 8*14 = 138

2A = 26

A=13