Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Algebra

Problem
1) Define the operation V as p V q = (p + q)/(2p + q).
What is 6 V 4 in lowest terms?
2) Rory knows he is 8 inches shorter than his sister. He's figured out that his height in inches is 7/8 her height in inches. How tall is he in inches?

3) Mrs. Pack notices that in her stamp drawer she still has unfinished rolls of old 8 cent stamps and 15 cent stamps. She needs to mail a package for which the postage is $0.78. What's the fewest number of 8 cent stamps and 15 cent stamps she can use to get the exact postage amount?
4) A TV station uses the following method for determining commercial time for any of its special 2 hour broadcasts. It divides the broadcast into 20 minute segments. In the first segment no commercials are aired. Then for each subsequent 20 minute segment the amount of time given to the special is reduced by 25% from the previous 20 minute segment. The remainder of the 20 minutes is given to commercials. In the first hour how much time is spent on commercials to the nearest second?
5) In the following pattern of rectangles, how many squares are needed to make the nth rectangle? Express your answer in terms of n.