Answer to the Problem of the Week

for the week of February 28, 2000

Solve the following problem between Monday and Friday. Then click on the icon below to e-mail your solution along with your name, city, and state.

The Store Problem
A man goes into a store and says to the owner: "Give me as much money as I have with me and I will spend $10."

It is done and the man repeats the operation at a second and a third store, after which he has no money left.

How much did he start with?


Solution:

The answer is $8.75

Let x = how much the man started with.
Then in the first store:
x + x - 10 is how much he had left.
In the second store:
(2x-10) + (2x-10) - 10 is how much is left
This simplifies to 4x - 30
In the third store:
(4x-30) + (4x-30) - 10 is how much is left
This simplifies to 8x - 70

So, 8x - 70 = 0 (no money left)
8x = 70
x = 70/8 or $8.75


Correctly solved by:

1. Richard Mocarski Winchester, VA
2. Chip Crawford Winchester, VA
3. Sam Stiebel Winchester, VA
4. Kirstine Wynn Winchester, VA
5. Elizabeth Cotter Oak Hill, VA
6. Tom Marino Winchester, VA
7. Court Pifer Winchester, VA
8. Joe Jenkins Winchester, VA
9. Eric Harding McLean, VA
10. Zinedine Zindane Marseille, France
11. John Pence Winchester, VA
12. Ryan Throckmorton Winchester, VA