Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 5 Algebra

Problem
Solution
1) Gemma is 12 years old. Gemma is five years older than Rebecca, and Jared is three times as old as Rebecca. How much older than Gemma is Jared? 1. If Gemma is 12 and is 5 years older than Rebecca, then Rebecca is 7 years old.
2. If Jared is 3 times as old as Rebecca, then he is 21.
3. Subtract Gemma's age from Jared's = 21 - 12 = 9 years.
2) Carson collects pennies, nickels, and dimes in a jar. He pulls out a handful of coins at random and counts them. If Carson pulls out 38 coins totaling $1.14 and he only has 1 nickel, how many of the coins are pennies? 1. Subtract the 5 cents from $1.14 = $1.09.
2. This is the sum of the pennies and dimes and now there are 37 coins left.
3. This is now a guess-and-check problem. Use this table: (make sure the number of pennies and dimes adds to 37 coins)
Guess ## dimes# penniesTotal $
1829$1.09
There are 29 pennies.
3) Reese is braiding several lengths of colored string together with a repeating pattern of green, blue, green, red, and purple. What will the color of the 47th braid be? 1. There are 5 colors in the repeating pattern.
2. Divide 47 by 5 and the remainder is 2.
3. This is the number of the 47th color in the pattern = blue.

Problem
Solution
4) A farm keeps chickens (with 2 legs) and pigs (with 4 legs) in a pen. There are a total of 55 chickens and pigs in the pen. There are a total of 178 legs amongst them all. How many pigs are in the pen? Wow! Another guess-and-check problem! Use this table: (make sure the number of heads adds to 55)
Guess ## Chickens# PigsTotal
heads
Total
feet
1213455178
There are 34 pigs.
5) How many times must you fold a piece of paper in half to create more than 500 layers? Each fold doubles the previous # of layers, so complete this sequence until you get to a number higher than 500:
    Folds:   1   2   3   4   5   6   7     8       9
    Layers: 2   4   8 16 32 64 128 256   512
# Folds = 9