systems of equations word problem

Question

Lea's school is selling tickets to a fall musical. On the first day of tickets sales the school sold 2 senior citizen tickets and 3 child tickets for a total of $21. The school took in $33 on the second day by selling 4 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Answer 1

Let's call Senior Citizen tickets S and Child tickets C.

2S + 3C = 21 and 4S + 3C = 33

Since you can't solve an equation with two variables, we have to get rid of one of the variables. Notice that both equations have 3C in them. So, we can subtract one equation from the other to get an equation that only has S's in it.

4S - 2S = 2S

3C - 3C = 0

33 - 21 = 12

So, 2S = 12

Divide both sides by 2: S = 6.

Now that we know the Senior Citizen tickets cost $6, we can plug that 6 back into one of the equations where we currently have S.

2(6) + 3C = 21

12 + 3C = 21

Subtract 12 from both sides: 3C = 9

Divide both sides by 3: C = 3

So Senior Citizen tickets cost $6 and Child tickets cost $3