the Walker and Baldwin families ordered lunch at the refreshment stand at the basketball game. The Walker family ordered 4 hot dogs and 3 cheeseburgers and paid $23.75. The Baldwin family ordered 6 hots dogs and 2 cheeseburgers and paid $25. Write a system of equations using h for hot dogs and c for cheeseburgers.

Question

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Answer 1

Let h represent the cost of a hot dog and c represent the cost of a cheeseburger.

From the information given, we can write the following two equations:

4h + 3c = 23.75 (for the Walker family)
6h + 2c = 25 (for the Baldwin family)

Answer 2

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Answer 3

To solve this system of equations, we can use the method of elimination:

Multiply the first equation by 2 to make the coefficients of c the same:
8h + 6c = 47.50

Multiply the second equation by 3 to make the coefficients of c the same:
18h + 6c = 75

Now we have the system of equations:
8h + 6c = 47.50
18h + 6c = 75

Subtract the first equation from the second equation:
10h = 27.50
h = 2.75

Now substitute h back into one of the original equations to solve for c. Using the first equation:
4(2.75) + 3c = 23.75
11 + 3c = 23.75
3c = 12.75
c = 4.25

Therefore, the cost of a hot dog is $2.75 and the cost of a cheeseburger is $4.25.