To determine how much Rosetta should receive after selling her house and paying off the mortgage, let's break down the relevant figures from her balance sheet.
1. House Value: The value of Rosetta's house is listed as \[tex]$150,000.
2. Mortgage: The outstanding mortgage amount is listed as \$[/tex]100,000.
When Rosetta sells her house, she will get the value of the house, which is \[tex]$150,000. However, she needs to use part of this amount to pay off the remaining mortgage, which is \$[/tex]100,000.
The amount she will receive after paying off the mortgage is calculated by subtracting the mortgage amount from the house value:
[tex]\[
\text{Amount to be received} = \text{House Value} - \text{Mortgage}
\][/tex]
[tex]\[
\text{Amount to be received} = \$150,000 - \$100,000
\][/tex]
[tex]\[
\text{Amount to be received} = \$50,000
\][/tex]
Therefore, after selling her house and paying off the mortgage, Rosetta should receive \$50,000. The correct answer is:
[tex]\[
\boxed{50,000}
\][/tex]
