FOR CHILDREN

PROBLEM # 1
The product of 3 brothers' ages is 175. Two are twins. How old is the other one?

FOR GROWNUPS

PROBLEM # 2
A snug-fitting belt is placed around the Earth's equator.  Suppose you added an extra 1 meter of length to the belt, held it at a point, and lifted until all the slack was gone.  How high above the Earth's surface would you then be?  That is, find h in figure below.

(Assume that the Earth is a perfect sphere of radius 6400 km, and that the belt material does not stretch.)

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SOLUTIONS TO PROBLEMS ON 01/25/07

FOR CHILDREN

PROBLEM # 1
What is the point of intersection of two straight lines represented by x+2y=4 and x+3y=5?

SOLUTION
(2,1).

FOR GROWNUPS

PROBLEM # 2
The vertices of a 3-4-5 right triangle are the centers of three mutually externally tangent circles. What is the sum of areas of these circles.

SOLUTION 
14 pi. 

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