# Monthly Archives: November 2012

## Sum of Two Reciprocals

The sum of two numbers is nine. The product of the same two numbers is thirty-eight. Find the sum of the reciprocals of these two numbers. Source: mathcontest.olemiss.edu 11/26/2012 SOLUTION Let and represent the two numbers. Answer: Advertisements

## Lucas Sequence

Consider the so-called Lucas sequence: , in which every number after the second is the sum of the two preceding numbers. Prove that not a single member of this sequence is divisible by . Source: NCTM Mathematics Teacher SOLUTION The … Continue reading

## Areas in Rectangle

Given rectangle , find the ratio of the area of region to the area of region . Source: NCTM Mathematics Teacher SOLUTION Area of region Area of region Since the diagonals of a rectangle bisect each other, the area of region … Continue reading

## Change For a Quarter

How many ways can you make change for a quarter? Source: NCTM Mathematics Teacher SOLUTION G. Polya in his book “How to Solve It” has a formula that calculates the number of ways to make change for a quarter equals . … Continue reading