To solve the system of equations given by:
- \( 4h + 4s = 10 \)
- \( 7h + 5s = 15 \)
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.