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.

Answer 1

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

Answer 2

what are the prices

Answer 3

Let's denote the price of a hot dog as x and the price of a cheeseburger as y.

From the first equation (4h + 3c = 23.75), we can divide it by 7 to simplify the equation,

0.57h + 0.43c = 3.39

From the second equation (6h + 2c = 25), we can divide by 2 to simplify the equation,

3h + c = 12.50

So, the prices are $0.57 for a hot dog and $0.43 for a cheeseburger.

Answer 4

but what are the prices

Answer 5

Let's solve the system of equations to find the prices of a hot dog and a cheeseburger.

From the first equation, 4h + 3c = 23.75, we can rewrite it as:

4h = 23.75 - 3c
h = (23.75 - 3c) / 4

Substitute this expression for h into the second equation, 6h + 2c = 25:

6((23.75 - 3c) / 4) + 2c = 25
(142.5 - 18c) / 4 + 2c = 25
142.5 - 18c + 8c = 100
-10c = -42.5
c = 4.25

Substitute c = 4.25 back into h = (23.75 - 3c) / 4:

h = (23.75 - 3(4.25)) / 4
h = (23.75 - 12.75) / 4
h = 11 / 4
h = 2.75

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