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.(1 point) Responses 7c = 23.75 and 8h = 25 7c = 23.75 and 8h = 25 4h − 3c = 23.75 and 6h − 2c = 25 4h − 3c = 23.75 and 6h − 2c = 25 4h + 3c = 23.75 and 6h + 2c = 25 4h + 3c = 23.75 and 6h + 2c = 25 h + c = 23.75 and h + c = 25 h + c = 23.75 and h + c = 25 Question 2 What are the prices of a hot dog and a cheeseburger? This question requires you to show your work. (2 points)

Answer 1

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

From the system of equations:
4h + 3c = 23.75
6h + 2c = 25

Solve the first equation for c:
3c = 23.75 - 4h
c = (23.75 - 4h) / 3

Now, substitute this expression for c into the second equation:
6h + 2((23.75 - 4h) / 3) = 25
6h + (47.5 - 8h) / 3 = 25
18h + 47.5 - 8h = 75
10h = 27.5
h = 2.75

Now, substitute h = 2.75 back into the first equation to find c:
4(2.75) + 3c = 23.75
11 + 3c = 23.75
3c = 12.75
c = 4.25

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