Answer to May 26, 2003 Problem
submitted by Bill Funk
from an 1866 Greenleaf book entitled
"Common School Arithmetic"

Five Daughters Problem


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