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

Answer 1

To solve the system of equations, we have the following two equations:

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

We can simplify the first equation by dividing all terms by 4:

\[
h + s = 2.5 \quad (1)
\]

Next, we'll express \( s \) in terms of \( h \) from equation (1):

\[
s = 2.5 - h \quad (2)
\]

Now we'll substitute equation (2) into the second equation:

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

This expands to:

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

Combining like terms gives:

\[
2h + 12.5 = 15
\]

Now, subtract 12.5 from both sides:

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

Dividing both sides by 2:

\[
h = 1.25
\]

Now, we can substitute \( h \) back into equation (2) to find \( s \):

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

Thus, the solution is:
\[
h = 1.25 \quad \text{(cost of a hot dog)}
\]
\[
s = 1.25 \quad \text{(cost of a soda)}
\]

So, the cost of both the hot dog and the soda is $1.25.