May 2015
Problem of the Month

Easy as A, B, C
from Alex Pintilie

If a + b + c = 7     and    


Determine the value of    

Solution to the Problem:

The answer is 19/10.

There is not enough information to solve for a, b, an c since you have three variables and only two equations.   However, you can answer the question!

I wrote a computer program to solve the problem, and I found that there are six possibilities for a, b, and c:

A	B	C
1	2	4
1	4	2
2	1	4
2	4	1
4	1	2
4	2	1

All six possibilities result in the same answer:

   

Sophie Sommer solved the problem algebraically.   Here is her solution:

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Chad Fore	Gate City, Virginia
3. Sophie Sommer	The Field School, Washington, DC
4. Brooks Garris	Lake View High School, Lake View, South Carolina
5. Dalton Stoddard	Mountain View High School, Mountain View, Wyoming
6. Faith Pfeifer	Mountain View High School, Mountain View, Wyoming
7. Michael Reilly	Silver Spring, Maryland

Send any comments or questions to: David Pleacher