Answer to the Problem of the Week
for the week of February 13, 2006

Sibling Rivalry
by Bob Stanton
Games Magazine December 2003

Four brothers spent an afternoon at a computer store.   Later, Ken said to Billy, "Did you notice that Sam and I spent the same amount of money as you and Pat?"

Billy replied, "No, I didn't, but I did notice that Sam and I spent twice as much as you and Pat."

Pat said to Billy, "That's nothing.   Sam and I spent three times as much as you and Ken."

Assuming that all purchases were in exact numbers of dollars and that no one spent less than $45 or more than $500, how much did each brother spend?


 

Solution to the Problem:

Ken spent $45, Billy spent $225, Pat spent $315, and Sam spent $495.

The relationships described in the problem can only be true if the ratio of spending of Ken : Billy : Pat : Sam is 1:5:7:11.

Multiplying by $45 (since no one spent less) yields the answer; it cannot be a higher number since multiplying by $46 will put Sam's total over $500.


Correctly solved by:

1. Sagar Patel Columbus, Georgia
2. Mike Singer Winchester, Virginia
3. Kshtij (Chris) Mehrotra Elgin, Illinois
4. James Alarie University of Michigan -- Flint
Flint, Michigan
5. Russell Beaty Columbus, Georgia
6. Praveen Nandamuru Columbus, Georgia
7. Carter Galbraith Columbus, Georgia
8. Magdy Essafty Alexandria, Egypt
9. Larry Schwartz Trumbull, Connecticut
10. David & Judy Dixon Bennettsville, South Carolina
11. Sharina Smith Newport News, Virginia
12. Neal Amos Columbus, Georgia
13. Kunal Singh Kendriya Vidyalaya
Happy Valley, Shilong, India
14. Javier Johnson ----------
15. Garrett Hix Columbus, Georgia
16. Kerry Barwick ----------
17. Laura Gronauer Winchester, Virginia
18. Julianne Harris Winchester, Virginia
19. Lauren Coles Chelmsford, Massachussetts
20. Ramakanth Reddy ----------
21. Emily Powell Winchester, Virginia
22. Billy Sutherland Winchester, Virginia
23. Maggie Morrison Winchester, Virginia