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
4
ℎ
+
4
𝑠
=
10

7h+5s=15
7
ℎ
+
5
𝑠
=
15

(1 point)
h=$
ℎ
=
$


s=$
𝑠
=
$


Check answerRemaining

Answer 1

To solve the system of linear equations given:

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

Let's simplify the first equation. We can divide everything by 4:

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

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

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

Next, we will substitute Equation 2 into Equation 1:

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

Expanding this gives:

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

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 \( h \), we can find \( s \) by substituting \( h = 1.25 \) back into Equation 2:

\[
s = 2.5 - 1.25 = 1.25
\]

Thus, the solution is:

\[
h = 1.25, \quad s = 1.25
\]

Final answers in decimal form:

- \( h = 1.25 \) (cost of a hot dog)
- \( s = 1.25 \) (cost of a soda)