FOR CHILDREN AND GROWNUPS

PROBLEM # 1
Calculate the minimum outside surface of a cylindrical bucket with an open upper side and which can hold 30 liters of water.

PROBLEM # 2
Circles with centers A and B have radii 3 and 8, respectively. The common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and AE = 5. What is CD?

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SOLUTIONS TO PROBLEMS ON 11/02/06

FOR CHILDREN

PROBLEM # 1
Radha and Sudha are saving for college. Radha starts with $a in her piggy bank and Sudha starts with $b in hers. Each week, Radha deposits $5 into her piggy bank and Sudha deposits $7 in hers. In 15 weeks, they will have the same amount. In 30 weeks, the ratio of Sudha's savings to Radha's is 8:7. Determine a+b.

SOLUTION
a+b = 90.

FOR GROWNUPS

PROBLEM # 2
A and B got into a fight. The probability that they will see each other on the nth day from now is 3/(3n+5). What is the probability that they will not see each other for the next 31 days.

SOLUTION 
5/98.

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