Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 6 Algebra

Problem
1) One angle of a triangle has a measurement of 70 degrees. The ratio of the other two angles of the triangle is 5:6. What are the measurements of the other two angles?

2) A group of scientists is duplicating cells for a science experiment. They observe that during each 10-minute period, one-quarter of the cells present died and the rest of the cells all doubled. If there were 32 cells initially, how many cells were there after 40 minutes?

3) There are 832 steps from the basement to the restaurant level of the Space Needle. You start out going up 25 steps every 20 seconds. After one minute you slow down to going up 24 steps every 20 seconds for the next minute, then 23 steps every 20 seconds in the next minute and so on. If this pattern continues, how long to the nearest minute will it take you to reach the restaurant?

4) Three watermelons and two cantaloupes weigh 32 pounds. Four watermelons and three cantaloupes weigh 44 pounds. All watermelons weigh the same and all cantaloupes weigh the same in this problem. What is the total weight of one watermelon and one cantaloupe?

5) King Kong climbed to the top of the 1250 foot tall Empire State Building. He would climb 150 feet, but then slip down 25 feet. How many feet total did King Kong climb up during his journey to get to the top?