I need help solving a word problem

Question

The schools that Trevon goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 13 child tickets for a total of $115. The school took in $69 on the second day by selling 8 senior citizen tickets and 3 child tickets. What is the price of each of one senior citizen ticket and one child ticket

Answer 1

You can use linear combination or substitution. I think linear combination is easier in this case. 

 

Let:

x=number senior citizen tickets sold

y=number child tickets sold

 

Your two equations will be

4x+13y=115

8x+3y=69

 

If you multiply the first equation by (-2), it will look like this:

 

-8x-26y=-230

8x+3y=69

 

Combining these equations:

 

-23y=-161

y=-161/-23

y=7

 

Substitute y=7 in to 4x+13y=115

4x+13(7)=115

4x+91=115

4x=24

x=24/4

x=6

Answer 2

Let x = the price of a children's ticket

Let y = the price of a senior ticket

13x + 4y = 115

3x + 8y = 69   Multiply the first equation by -2 and then add the two equations together.

 

-26x - 8y = -230

  3x + 8y = 69

       -23x = -161

           x = $7

3(7) + 8y = 69

  21 + 8y = 69

          8y = 48

            y = $6