Tim bought 3 hamburgers and 4 hot dogs for $19. John bought 5 hamburgers and 2 hot dogs for $20. How much is one hot dog and one hamburger each?

Work Shown:

x = cost for one hamburger

y = cost for one hot dog

3x = cost for 3 hamburgers

4y = cost for 4 hot dogs

3x+4y = total cost for 3 hamburgers, 4 hot dogs

3x+4y = 19

5x = cost for 5 hamburgers

2y = cost for 2 hot dogs

5x+2y = total cost for 5 hamburgers, 2 hot dogs

5x+2y = 20

The equations we have set up are

3x+4y = 19

5x+2y = 20

If we multiply everything in the second equation by 2, then we have 5x+2y = 20 turn into 10x+4y = 40

So we have this equivalent system

3x+4y = 19

10x+4y = 40

Subtract straight down to get -7x = -21 which solves to x = 3.

use the value of x to find y

3x+4y = 19

3*3+4y = 19

9+4y = 19

4y = 19-9

4y = 10

y = 10/4

y = 2.50