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.

Question

4h+4s=10


7h+5s=15


(1 point)
h=$

s=$

Answer 1

To solve the system of equations

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

we can start by simplifying the first equation.

Step 1: Simplify the first equation

Divide the entire equation by 4:

\[ h + s = \frac{10}{4} \implies h + s = 2.5 \]

So, we can write this as:

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

Step 2: Solve for \(s\)

From equation (1):

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

Step 3: Substitute \(s\) in the second equation

Now substitute equation (2) into the second equation:

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

Now, distribute:

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

Combining like terms gives:

\[ 2h + 12.5 = 15 \]

Step 4: Solve for \(h\)

Subtract 12.5 from both sides:

\[ 2h = 15 - 12.5 \] \[ 2h = 2.5 \] \[ h = \frac{2.5}{2} = 1.25 \]

Step 5: Substitute \(h\) back into equation (2)

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

\[ s = 2.5 - 1.25 = 1.25 \]

Step 6: Write the final answer

Thus, the solutions are:

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

So the final answer is:

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