Answer:
$300
Step-by-step explanation:
The total value gained V is given by sum of the value gained when buying the book (B) added to the value gained when selling the book (S).
The value gained at purchase is given by the difference between the willingness to pay and the actual amount paid:
![B=\$450 -\$200\\B= \$250](https://img.qammunity.org/2021/formulas/business/college/ok8www4dley7699gy5zzfc1ge4468ngfkf.png)
The value gained when selling the book is given by the difference between the amount received from selling and the value of keeping the book:
![S= 0.5*\$200 - \$50\\S=\$50](https://img.qammunity.org/2021/formulas/business/college/dz0ebogo26igksggvxr71ve0nafjbja348.png)
The total value gained is:
![V= B+S\\V=\$250+\$50\\V=\$300](https://img.qammunity.org/2021/formulas/business/college/u50gsb6tm8feqsezg32w9jxf840emxjlf8.png)
You have gained $300 in total value.