page 19 of 20

Question

Real-World Systems of Equations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
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.

4h+4s=10


7h+5s=15


(1 point)
h=$

s=$

Remaining Attempts : 3

Answer 1

To solve the system of equations, we'll start with the given equations:

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

We can simplify the first equation:

\[ 4h + 4s = 10 \implies h + s = 2.5 \quad \text{(divide everything by 4)} \]

Now we have a simpler equation to work with:

1. \( h + s = 2.5 \) (Equation 1)
2. \( 7h + 5s = 15 \) (Equation 2)

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

\[ s = 2.5 - h \]

Next, we will substitute \( s \) into Equation 2:

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

Now, distribute the 5:

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

Combine like terms:

\[ 2h + 12.5 = 15 \]

Now, isolate \( h \):

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

Now that we have \( h \), we can find \( s \):

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

So the solution is:

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

Final Answers:

• \( h = $1.25 \)
• \( s = $1.25 \)