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
ℎ
for hot dogs and c
for cheeseburgers.(1 point)
Responses
4h − 3c = 23.75
4
ℎ
−
3
=
23.75
and 6h − 2c = 25
6
ℎ
−
2
=
25
4h − 3c = 23.75
4
ℎ
−
3
=
23.75
and 6h − 2c = 25
6
ℎ
−
2
=
25
7c = 23.75
7
=
23.75
and 8h = 25
8
ℎ
=
25
7c = 23.75
7
=
23.75
and 8h = 25
8
ℎ
=
25
h + c = 23.75
ℎ
+
=
23.75
and h + c = 25
ℎ
+
=
25
h + c = 23.75
ℎ
+
=
23.75
and h + c = 25
ℎ
+
=
25
4h + 3c = 23.75
4
ℎ
+
3
=
23.75
and 6h + 2c = 25
6
ℎ
+
2
=
25
4h + 3c = 23.75
4
ℎ
+
3
=
23.75
and 6h + 2c = 25
6
ℎ
+
2
=
25
Question 2
What are the prices of a hot dog and a cheeseburger?
This question requires you to show your work.
(2 points)
To find the prices of a hot dog and a cheeseburger, we can solve the system of equations:
4h - 3c = 23.75
6h - 2c = 25
First, let's solve the first equation for h:
4h - 3c = 23.75
4h = 23.75 + 3c
h = (23.75 + 3c) / 4
Now, 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
10c = -42.5
c = -4.25
Now, substitute back to find the price of a hot dog:
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.