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 linear equations given by

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

we will first simplify the first equation by dividing through by 4:

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

Now we can express \(s\) in terms of \(h\):

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

Next, we will substitute equation (4) into equation (2):

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

Expanding this:

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

Now, combine like terms:

\[
2h + 12.5 = 15
\]

Subtract 12.5 from both sides:

\[
2h = 2.5
\]

Now, divide by 2:

\[
h = 1.25
\]

Now that we have the value of \(h\), let's substitute back into equation (4) to find \(s\):

\[
s = 2.5 - 1.25 = 1.25
\]

Thus, the final prices are:

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

Both prices are \(1.25\).