A gentleman has 5 daughters: Emily, Jane, Betsy, Abigail, and Nancy,
whose fortunes are as follows:
The first two and the last two have $19,000;
the first four, $19,200;
the last four, $20,000;
the first and the last three, $20,500;
the first three and the last, $21,300.
What is the fortune of each?"
Solution to Problem:
The five daughters had the following fortunes:Emily -- $5,000
Jane -- $4,500
Betsy -- $6,000
Abigail -- $3,700
Nancy -- $5,800
To solve this problem, set up five equations with five
variables and solve simultaneously. The five equations are:
E + J + A + N | = | 19,000 |
E + J + B + A | = | 19,200 |
J + B + A + N | = | 20,000 |
E + B + A + N | = | 20,500 |
E + J + B + N | = | 21,300 |
Correctly solved by:
1. Rick Jones | Kennett Square, Pennsylvania |
2. Richard Johnson | La Jolla, California |
3. Walt Arrison | Philadelphia, Pennsylvania |
4. Misty Carlisle | Winchester, Virginia |
5. Jaime Garcia | Winchester, Virginia |
6. John Beasley | Winchester, Virginia |
7. Jeffrey Gaither | Winchester, Virginia |
8. Bob Hearn | Winchester, Virginia |
9. Rich Murray | Ridgetown, Ontario Canada |
10. Matt Stillwagon | Winchester, Virginia |
11. Andrew Winkelhake | --------- |
12. James Alarie | University of Michigan -- Flint Flint, Michigan |
13. David and Judy Dixon | Bennettsville, South Carolina |
14. Joshua Folb | Winchester, Virginia |