Certainly! Let's break down the steps to determine how much Rosetta should receive if she sells her house and pays off the mortgage.
1. Determine the value of the house:
- The value of the house is listed as \[tex]$150,000.
2. Determine the amount owed on the mortgage:
- The mortgage value is \$[/tex]100,000.
3. Calculate the net amount received from selling the house:
- When Rosetta sells the house, she needs to pay off the mortgage. Thus, the net amount she receives will be the house value minus the mortgage value.
Given the values:
[tex]\[
\text{House Value} = \$150,000
\][/tex]
[tex]\[
\text{Mortgage Value} = \$100,000
\][/tex]
To find the net amount received:
[tex]\[
\text{Net Amount} = \text{House Value} - \text{Mortgage Value}
\][/tex]
Substituting the given values:
[tex]\[
\text{Net Amount} = 150,000 - 100,000 = 50,000
\][/tex]
Thus, after selling the house and paying off the mortgage, Rosetta will receive \[tex]$50,000. This matches the numerical result presented.
So, the correct answer is:
\[
\$[/tex] 50,000
\]
