Sue is selling tickets for the circus. On day one she sold 4 senior tickets and 2 children's tickets and made $80. On day two she sold 5 senior tickets and 7 children's tickets making $145. how much were each senior and child's tickets?

**Write two equations based on the information given:**

4x + 2y = 80

5x + 7y = 145

where x = senior's tickets and y = children's tickets

**We now have two equations with two variables. We could solve this a number of ways. I will use substitution:
**

Solve for y in the first equation:

4x + 2y = 80

y = (80 – 4x) / 2 = 40 – 2x

Now plug y = 40 – 2x into the second equation:

5x + 7y = 145

5x + 7(40 – 2x) = 145

5x + 280 – 14x = 145

-9x = -135

x = 15

Now that we know x = 15, we can solve for y in either one of the original equations.

4x + 2y = 80

4(15) + 2y = 80

2y = 20

y = 10

**Answer: x = 15, y = 10. (Senior’s tickets: $15, children’s tickets: $10)**

You should verify that you have the right answer by substituting the values found for x and y back into the original equations.