May 26, 2003
Problem of the Month

submitted by Bill Funk   from an 1866 Greenleaf book entitled   "Common School Arithmetic"

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 the 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

Send any comments or questions to: David Pleacher