Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Algebra

Problem
Hint
1) Define the operation V as p V q =
(p + q)/(2p + q).
What is 6 V 4 in lowest terms?
1. In the expression for V, p = 6 and q = 4.
2. Put these values into the equation for V and solve = _____
3. Reduce to 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? 1. If he is 7/8ths of his sister's height then what remains is the fraction _____.
2. This fraction of his sister's height is 8 inches.
3. His sister's height is ____ inches.
4. His height is ____ 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?
1. Divide 78 cents by 15 to get the number of 15 cent stamps = ____
2. Compute the remainder by subtracting the value of this many 15 cent stamps from 78 cents = ___.
3. If this remainder is not a multiple of 8, reduce the number of 15 stamps by 1 and repeat until you get a remainder that is divisible by 8
4. Mrs. Pack needs ___ 8 cent stamps and ___ 15 cent stamps.

Problem
Hint
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? Fill out this table:
Time segment
(mins)
% special% commercialCommercial
time (mins)
0-20100%0% 0
21-40    
41-60    
Total commercial time = _____ minutes.
5) In the following pattern of rectangles, how many squares are needed to make the nth rectangle? Express your answer in terms of n.
1. For each n (1 - 3) write out the number of cubes on the bottom row:
              n = 1     2     3
    # cubes ___   ___   ___
2. The expression for this is ____ in terms of n.
3. Notice that the number of layers is equal to n.
    and that you already have 1 layer accounted for.
4. The expression for the nth term is _____________.