Question

The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let represent the cost of a hot dog and represent the cost of the soda. Write the answers in decimal form. Solve the system of linear equations.

4h+4s=10
7h+5s=15

h=$
s=$

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of linear equations, we can use the method of substitution or elimination. Here, we will use the substitution method:

First, rearrange the equations to solve for one variable:
From the first equation: 4h + 4s = 10
Divide by 4: h + s = 2.5
From the second equation: 7h + 5s = 15
Solve for h: 7h = 15 - 5s -> h = (15 - 5s)/7

Substitute the value of h into the first equation:
(15 - 5s)/7 + s = 2.5
15 - 5s + 7s = 17.5
2s = 2.5
s = 1.25

Now, substitute the value of s back into h = (15 - 5s)/7:
h = (15 - 5(1.25))/7 = 1.25

Therefore, the cost of a hot dog (h) is $1.25 and the cost of the soda (s) is $1.25.