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 linear equations:

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

Let's first simplify the first equation.

Divide the entire first equation by 4:

\[
h + s = \frac{10}{4}
\]
\[
h + s = 2.5 \quad \text{(Equation 1)}
\]

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

\[
s = 2.5 - h \quad \text{(Equation 2)}
\]

Next, substitute Equation 2 into the second equation:

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

Distributing the 5:

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

Combine like terms:

\[
2h + 12.5 = 15
\]

Now, subtract 12.5 from both sides:

\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]

Divide both sides by 2:

\[
h = 1.25
\]

Now, substitute \(h\) back into Equation 2 to find \(s\):

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

Thus, the solution is:

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

**Final answers:**
\(h = \$1.25\)
\(s = \$1.25\)