Question

Two movie tickets and three concert tickets cost $21. Three movie tickets and 2 concert tickets cost $19. Each ticket costs a whole number of dollars.

How much does 1 movie ticket cost?
How much does 1 concert ticket cost?

Answer 1

movie ticket = $3 concert = 5$

Explanation:

Movie = m Concert = c

2m + 3c = 21

3m + 2c = 19

First find the value of one of the variables by isolating them

3m + 2c = 19

3m = 19 - 2c

m = 19/3 - 2c/3

Input the value for that variable into the other problem

2(19/3 - 2c/3) + 3c = 21

38/3 - 4c/3 + 3c = 21

38/3 + 5c/3 = 21

5c/3 = 21 - 38/3

5c/3 = 63/3 - 38/3

5c/3 = 25/3

5c = 25

c = 5

Now that we've found the actual value for c plug that into any of the 2 problems and solve for m

3m + 2(5) = 19

3m + 10 = 19

3m = 9

m = 3

Movie = 3 Concert = 5

Answer 2

one concert ticket=5 and one movie ticket=3