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 for cheeseburgers.(1 point)
Responses
A. 7c = 23.75 and 8h = 25
B. h + c = 23.75
and h + c = 25
C. 4h − 3c = 23.75
and 6h − 2c = 25
D. 4h + 3c = 23.75
and 6h + 2c = 25
C. 4h − 3c = 23.75
and 6h − 2c = 25
Show your work for this problem
Let h represent the cost of a hot dog and c represent the cost of a cheeseburger.
From the information given:
- The Walker family ordered 4 hot dogs and 3 cheeseburgers and paid $23.75. This can be represented as: 4h + 3c = 23.75
- The Baldwin family ordered 6 hot dogs and 2 cheeseburgers and paid $25. This can be represented as: 6h + 2c = 25
So, the system of equations is:
4h + 3c = 23.75
6h + 2c = 25
Therefore, the correct answer is:
C. 4h − 3c = 23.75
and 6h − 2c = 25
What are the prices of a hot dog and a cheeseburger?
$4.25 $2.00 $5.00 $2.75
Cheeseburger 0 0 0 0
Hot dog 0 0 0 0
Let's solve the system of equations:
4h - 3c = 23.75 (Equation 1)
6h - 2c = 25 (Equation 2)
From Equation 1:
4h = 23.75 + 3c
h = (23.75 + 3c)/4
Substitute the value of h in Equation 2:
6(23.75 + 3c)/4 - 2c = 25
(142.5 + 18c)/4 - 2c = 25
142.5 + 18c - 8c = 100
142.5 + 10c = 100
10c = 100 - 142.5
10c = -42.5
c = -4.25
Substitute c back into Equation 1:
4h - 3(-4.25) = 23.75
4h + 12.75 = 23.75
4h = 23.75 - 12.75
4h = 11
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.