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