FOR CHILDREN

PROBLEM # 1
Ann purchased a house for $ 160312. She wants to sell it for a profit of exactly 12%. However, she does not want to sell it herself. She wants a Real Estate Agent to sell it for her. The Agent must make a commission of exactly 5.5% (in addition to Ann's 12% profit). How much must the Agent sell the house for? Give your answer to the nearest dollar.

FOR GROWNUPS

PROBLEM # 2
What is the limit of the function
f(x) = (4 - x^2) / (3 - sqrt(x^2 + 5))
as x tends to 2.

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SOLUTIONS TO PROBLEMS ON 01/12/06

FOR CHILDREN

PROBLEM # 1
You have a large number of iron balls, all exactly two inches in diameter, that you need to move. You need to pack them into a large wooden rectangular crate that is 24.9 inches long, 22.8 inches wide, and 14 inches deep. What is the greatest number of the balls that can be packed into the crate? 

SOLUTION
924.

FOR GROWNUPS

PROBLEM # 2
For 0 < x <2 pi, what is the sum of all values of x that satify the equation:
sin(2x) = cos(x).

SOLUTION
3 pi.

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