Question

the booster club is selling refreshments the following system of linear equations models. The concession stand prices represent the cost of a hotdog and represent the cost of the soda right that answers in decimal form solve the system of linear equations.

4h + 4s =10
7h + 5s =15

h= ?
s = ?

Answer 1

To solve the system of linear equations:

1. **Equations:**
\[
4h + 4s = 10 \quad (1)
\]
\[
7h + 5s = 15 \quad (2)
\]

2. **Simplify Equation (1):**
We can simplify the first equation by dividing everything by 4:
\[
h + s = 2.5 \quad (3)
\]

3. **Express \( s \) in terms of \( h \):**
From equation (3), we can express \( s \):
\[
s = 2.5 - h \quad (4)
\]

4. **Substitute \( s \) into Equation (2):**
Substitute equation (4) into equation (2):
\[
7h + 5(2.5 - h) = 15
\]
Distributing:
\[
7h + 12.5 - 5h = 15
\]
Combine like terms:
\[
2h + 12.5 = 15
\]
Subtract \( 12.5 \) from both sides:
\[
2h = 2.5
\]
Divide by 2:
\[
h = 1.25
\]

5. **Substitute \( h \) back into Equation (4) to find \( s \):**
Substitute \( h = 1.25 \) back into equation (4):
\[
s = 2.5 - 1.25
\]
\[
s = 1.25
\]

So, the solutions are:
\[
h = 1.25
\]
\[
s = 1.25
\]

Thus, the cost of a hotdog is **$1.25** and the cost of a soda is **$1.25**.