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

Question

for hot dogs and c
for cheeseburgers.

Answer 1

4h + 3c = 23.75
6h + 2c = 25

Answer 2

What are the prices of a hot dog and a cheeseburger?

Answer 3

To solve for the prices of a hot dog and a cheeseburger, we can solve the system of equations:

4h + 3c = 23.75
6h + 2c = 25

We can solve this system by elimination or substitution. Let's use the substitution method:

From the first equation, we can rearrange it to solve for h in terms of c:
4h = 23.75 - 3c
h = (23.75 - 3c) / 4

Now, we substitute this expression for h into the second equation:
6((23.75 - 3c) / 4) + 2c = 25
(142.5 - 18c) / 4 + 2c = 25
142.5 - 18c + 8c = 100
142.5 - 10c = 100
-10c = -42.5
c = 4.25

Now that we have the price of a cheeseburger, we can substitute this back into the first equation to solve for the price of a hot dog:
4h + 3(4.25) = 23.75
4h + 12.75 = 23.75
4h = 11
h = 2.75

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