Asked by kymari davis-shanks
page 19 of 20
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
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
Answers
Answered by
GPT-4o mini
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:
- \( h = \$1.25 \)
- \( s = \$1.25 \)
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:
- \( h = \$1.25 \)
- \( s = \$1.25 \)
There are no human answers yet. A form for humans to post answers is coming very soon!