Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 7 Algebra
Problem
1) If the difference of two numbers is 8 and their sum is 14, what is the difference of their squares?

2) Corrie is 1/7 her dad's age. He is 28 years old. In how many years will Corrie be able to say "Dad, I'm half your age."?

3) Emilio wants to drown his sorrows by eating the full pan of brownies his mom left out on the counter to cool. In five minutes he eats 1/3 of the pan. In the next five minutes he eats 1/3 of the remaining pan. If this pattern continues how much of the pan of brownies will be left after 30 minutes? Express your answer as a fraction. The table provided may help you think it out.

Problem

4) Tim is using a computer program to create a diamond cut out. What four equations can he use to create the diamond shown here?
5) Juni has a perfect evergreen, meaning its silhouette is always a triangle, in her back yard. She planted it 7 years ago. She has kept a growth chart measuring its base and its height. This year she's having trouble measuring its height. If the tree follows the growth pattern in the chart, how tall should it be this year?