Question

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Real-World Systems of Equations Practice
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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=$

Remaining Attempts : 3

Answer 1

To solve the system of equations, we'll start with the given equations:

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

We can simplify the first equation:

\[
4h + 4s = 10 \implies h + s = 2.5 \quad \text{(divide everything by 4)}
\]

Now we have a simpler equation to work with:

1. \( h + s = 2.5 \) (Equation 1)
2. \( 7h + 5s = 15 \) (Equation 2)

From Equation 1, we can express \( s \) in terms of \( h \):

\[
s = 2.5 - h
\]

Next, we will substitute \( s \) 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 find \( s \):

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

So the solution is:

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

Final Answers:

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