Question

At the baseball game the Kacanich family purchased 3 hot dogs and 2 cheeseburgers and paid $31.25. The Nisbet family purchased 5 hot dogs and 2 cheeseburgers and paid $41.75. Write and solve a linear system to find the cost of each hot dog and each cheeseburger.

Answer 1

Let x be the cost of a hot dog and y be the cost of a cheeseburger. Then we can set up the following system of equations:

3x + 2y = 31.25

5x + 2y = 41.75

We can solve for one of the variables by subtracting the first equation from the second:

5x + 2y - (3x + 2y) = 41.75 - 31.25

2x = 10

x = 5

Substituting x = 5 into either of the equations above gives:

3(5) + 2y = 31.25

15 + 2y = 31.25

2y = 16.25

y = 8.125

Therefore, a hot dog costs $5 and a cheeseburger costs $8.125.