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 given by:

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

We can start with Equation 1. We can simplify it by dividing everything by 4:

\[
h + s = 2.5 \quad (Equation 3)
\]

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

\[
s = 2.5 - h \quad (Equation 4)
\]

Next, we substitute Equation 4 into Equation 2:

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

Now, distribute the 5:

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

Combine like terms:

\[
2h + 12.5 = 15
\]

Now, isolate \( h \):

\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]
\[
h = \frac{2.5}{2} = 1.25
\]

Now that we have \( h \), we can plug it back into Equation 4 to find \( s \):

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

So, the solution is:

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

Finally, in decimal form:

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