Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Algebra
Problem
1)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 during 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?

2) 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 weight of two watermelons and one cantaloupe?

3) 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?

Problem
4) A special four digit number has the following traits:
  • All of the digits are different
  • The digits in the tens place is 3 times the digit in the hundredths place.
  • The digits are in descending order, so the digit in the tens place is greater than the digit in the ones place, the digit in the ones place is greater than the digit in the tenths place and so on.
  • The sum of the digits is 27.

5) How many integers satisfy (n - 4)(n + 6) ≤ 0?