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


(1 point)
h=$

s=$

1 answer

To solve the system of equations given by:

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

we can simplify the first equation and then solve the two equations together.

Step 1: Simplify the first equation

The first equation can be simplified by dividing all terms by 4:

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

Step 2: Express one variable in terms of the other

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

\[ s = 2.5 - h \quad \text{(Equation 3)} \]

Step 3: Substitute into the second equation

Now substitute Equation 3 into the second equation:

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

Now simplify:

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

Combine like terms:

\[ 2h + 12.5 = 15 \]

Step 4: Solve for \( h \)

Now, isolate \( h \):

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

Step 5: Substitute back to find \( s \)

Now, substitute \( h = 1.25 \) back into Equation 3 to find \( s \):

\[ s = 2.5 - 1.25 = 1.25 \]

Final Answers

Thus, the costs are:

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

Summary

The cost of a hot dog \( h \) is $1.25 and the cost of a soda \( s \) is $1.25.