To determine how much Rosetta should receive after selling her house and paying off the mortgage, let's break down the problem step-by-step.
1. Determine the value of Rosetta's house:
- The house is valued at \[tex]$150,000.
2. Determine the outstanding mortgage loan:
- The mortgage loan amounts to \$[/tex]100,000.
3. Calculate the amount Rosetta should receive after paying off the mortgage:
- Subtract the mortgage loan amount from the house value.
[tex]\[ \text{Amount received} = \text{House value} - \text{Mortgage loan} \][/tex]
[tex]\[ \text{Amount received} = \$150,000 - \$100,000 \][/tex]
[tex]\[ \text{Amount received} = \$50,000 \][/tex]
So, after selling her house and paying off the mortgage, Rosetta should receive \[tex]$50,000.
The correct answer is:
\[
\$[/tex] 50,000
\]