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

(1 point)
h=$

s=$

Answer 1

To solve the system of linear equations:

1. **Equations:**
\[
4h + 4s = 10 \quad \text{(Equation 1)}
\]
\[
7h + 5s = 15 \quad \text{(Equation 2)}
\]

2. **Simplify Equation 1:**
Dividing the entire first equation by 4:
\[
h + s = 2.5 \quad \text{(Equation 1 simplified)}
\]

3. **Express one variable in terms of the other from Equation 1:**
\[
s = 2.5 - h
\]

4. **Substitute into Equation 2:**
Substitute \( s \) into Equation 2:
\[
7h + 5(2.5 - h) = 15
\]
Simplifying:
\[
7h + 12.5 - 5h = 15
\]
\[
2h + 12.5 = 15
\]
\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]
\[
h = 1.25
\]

5. **Substitute \( h \) back to find \( s \):**
Using \( h = 1.25 \) in the simplified Equation 1:
\[
s = 2.5 - 1.25 = 1.25
\]

6. **Final Answer:**
\[
h = 1.25
\]
\[
s = 1.25
\]

Thus, the costs are:
\[
h = \$1.25
\]
\[
s = \$1.25
\]