Question

The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let h represent the cost of a hot dog and s 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 equations:

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

First, we can simplify the first equation. Divide the entire equation by 4:

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

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

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

Next, we substitute Equation 3 into the second equation:

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

Distribute the 5:

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

Combine like terms:

\[
2h + 12.5 = 15
\]

Now, isolate \( h \):

\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]
\[
h = 1.25
\]

Now, substitute \( h = 1.25 \) back into Equation 3 to find \( s \):

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

Thus, the final answer is:

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

So, in decimal form:

- \( h = \$1.25 \)
- \( s = \$1.25 \)