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

Answer 1

To solve the system of equations given by:

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

we will follow these steps:

### Step 1: Simplify the first equation
From the first equation, we can simplify it by dividing each term by 4:

\[
h + s = 2.5
\]

### Step 2: Express one variable in terms of the other
We can express \( s \) in terms of \( h \) from this simplified equation:

\[
s = 2.5 - h
\]

### Step 3: Substitute into the second equation
Next, substitute \( s \) into the second equation:

\[
7h + 5s = 15
\]

Replacing \( s \):

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

### Step 4: Distribute and combine like terms

Calculating inside the parentheses:

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

Combine like terms:

\[
2h + 12.5 = 15
\]

### Step 5: Solve for \( h \)

Now, subtract 12.5 from both sides:

\[
2h = 2.5
\]

Now divide by 2:

\[
h = 1.25
\]

### Step 6: Solve for \( s \)

Now substitute \( h \) back into the equation for \( s \):

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

### Final Answer:

Thus, the cost of a hot dog \( h \) and the cost of a soda \( s \) are both:

\[
h = 1.25 \quad \text{(cost of hot dog)}
\]
\[
s = 1.25 \quad \text{(cost of soda)}
\]

In decimal form, the solutions are:

**Cost of hot dog: $1.25**
**Cost of soda: $1.25**