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 equations given by:

1. \( 4h + 4s = 10 \)
2. \( 7h + 5s = 15 \)

we can simplify the first equation and then solve the two equations together.

### Step 1: Simplify the first equation

The first equation can be simplified by dividing all terms by 4:

\[
h + s = 2.5 \quad \text{(Equation 1)}
\]

### Step 2: Express one variable in terms of the other

From Equation 1, we can express \( s \) in terms of \( h \):

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

### Step 3: Substitute into the second equation

Now substitute Equation 3 into the second equation:

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

Now simplify:

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

Combine like terms:

\[
2h + 12.5 = 15
\]

### Step 4: Solve for \( h \)

Now, isolate \( h \):

\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]
\[
h = \frac{2.5}{2} = 1.25
\]

### Step 5: Substitute back to find \( s \)

Now, substitute \( h = 1.25 \) back into Equation 3 to find \( s \):

\[
s = 2.5 - 1.25 = 1.25
\]

### Final Answers

Thus, the costs are:

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

### Summary

The cost of a hot dog \( h \) is **$1.25** and the cost of a soda \( s \) is **$1.25**.