MATC Mathematics Club
Volume 8 Solutions Page

The Puzzle Corner of the MATC Mathematics Club
Madison Area Technical College
Madison, Wisconsin


Spring 2005 Problem Sets

Problem Set #1, Volume #08
1. Find all possible sets of four consecutive integers having the property that the sum of the cubes of the smallest three is equal to the cube of the largest.


2. Find the value of k for which the two equations  

   (x - 2)4 - (x - 2) = 0    and    x2 - kx + k = 0

have two roots in common.


3. Find all ordered pairs of integers (x, y) which satisfy x2 + 4x + y2 = 9.


4. The sum of the ages of the members of a family is currently 75 years, where the family consists of a mother, father, son, and daughter.  Six years ago, the sum of the ages of the family members was 53 years.  If the father is four years older than the mother, and the daughter is three years older that the son, find the current age of the father.


5. Express in simplest form:




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Mathematics Club

If you are interested, email Jeganathan "Sri" Sriskandarajah ( ) or contact him in room 211G.    Watch this page and the student bulletin for further announcements.


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