Answer to February 9, 2004 Problem

The Chicken Soup Problem

 
In the comic strip below, determine the values of the variables X and Y which will make the price of the book equal to $25.00 (when rounded to the nearest penny -- but don't round until the very end!). The values for X and Y must be positive integers (whole numbers).

In the comic, please note that the lowercase x is the multiplication symbol and the uppercase X is the variable. Be careful -- you must use the correct order of operations to solve this! (If you have forgotten that order, check out the algebra lesson plans section of this math page -- or use the old saying, "Please Excuse My Dear Aunt Sally.")

 

Solution to the Problem:

There were many correct answers. Some of them are shown in the table below:
X Y price price (rounded)
    2,312,925   50   $24.9965592         $25.00
    2,913,509   54   $25.00094630         $25.00
    6,621,778   71   $25.00100670        $25.00
  10,200,732   82   $25.00012251         $25.00
  13,941,487   91   $25.00042022         $25.00
  21,416,485 105   $25.00096806         $25.00
  36,133,233 125   $25.00035995         $25.00
  43,524,204 133   $25.00029400         $25.00
265,455,169 243   $24.99978995         $25.00

Dave Smith wrote a program to solve this and found 369 solutions between Y = 1 and Y =2,000. The most precise was y=912, x=14,033,183,297, cost= 25.000009004.


Correctly solved by:

1. Jeffrey Gaither Winchester, Virginia
2. John Funk (sent in 6 correct solutions) Ventura, California
3. Dave Smith (sent in 369 correct solutions) Toledo, Ohio
4. Matthew Reames Roanoke, Virginia
5. John Beasley Winchester, Virginia