Real-World Systems of Equations Practice

Question

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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


(1 point)
h=$

s=$

Answer 1

To solve the system of linear equations given:

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

We can simplify the first equation by dividing everything by 4:

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

Now we rearrange Equation 1 to express \( s \) in terms of \( h \):

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

Next, we can substitute Equation 3 into the second equation (Equation 2):

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

Distributing the 5 in the equation:

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

Now, combine like terms:

\[ 2h + 12.5 = 15 \]

Subtract 12.5 from both sides:

\[ 2h = 2.5 \]

Now divide by 2:

\[ h = 1.25 \]

Now that we have the value of \( h \), substitute it back into Equation 3 to find \( s \):

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

Thus, the costs are:

\[ h = 1.25, \text{and} , s = 1.25 \]

In decimal form:

• \( h = $1.25 \)
• \( s = $1.25 \)

Final answers: \[ h = 1.25 \quad s = 1.25 \]