## Answer :

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]