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 given by:

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

we can start by simplifying equation (1).

**Step 1: Simplify Equation (1)**

Divide the entire equation by 4:

\[
h + s = 2.5 \quad \text{(3)}
\]

**Step 2: Rearrange Equation (3) to isolate s**

From equation (3), we can express \( s \) in terms of \( h \):

\[
s = 2.5 - h \quad \text{(4)}
\]

**Step 3: Substitute (4) into Equation (2)**

Now substitute \( s \) from equation (4) into equation (2):

\[
7h + 5(2.5 - h) = 15
\]

Distributing the 5:

\[
7h + 12.5 - 5h = 15
\]

Combine like terms:

\[
2h + 12.5 = 15
\]

**Step 4: Solve for h**

Subtract 12.5 from both sides:

\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]

Now divide by 2:

\[
h = \frac{2.5}{2} = 1.25
\]

**Step 5: Find s using (4)**

Now substitute \( h = 1.25 \) back into equation (4):

\[
s = 2.5 - 1.25
\]
\[
s = 1.25
\]

**Final Answer**

Thus, the costs of the hot dog and soda are:

\[
h = 1.25
\]
\[
s = 1.25
\]

So the final answers are:
- \( h = \$1.25 \)
- \( s = \$1.25 \)