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:

• \( h = $1.25 \)
• \( s = $1.25 \)