Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 7 Algebra

Problem
1) Rudi and Ria go to the gym to do some weight lifting. Rudi goes first on the bench press, loading on three identical weights on each end of the bar. Ria can't lift as much and replaces each of the weights with weights that are 15 lbs lighter. If she is pressing 94 lbs total, what was Rudi pressing?

2) Megan wants to buy some bracelets and necklaces. Each bracelet is $8 and each necklace is $12. She buys a total of 12 items. How many of each did she buy if she has $100 to spend? Disregard sales tax.

3) I'm a mystery number. If you multiply me by 4 and then add 3 the result is the same number if you first add 4 to me and then multiply the result by 3. What number am I?

Problem
4) Consider the pattern of arrangements of squares. The perimeter of the 1st arrangement is 4 units. What is the perimeter of the 10th arrangement of squares?
5) 14 monkeys are bouncing on the bed and one falls off every 2 minutes. Create a graph with appropriate scale that expresses this problem on the coordinate system provided on the answer sheet. The graph should show the x and y intercepts. What is a linear equation that passes through the integer points on the graph?