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.")
Sorry, the comic strip is no longer available.
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 |