Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Algebra

Problem

1) Lucy is riding an elevator up a very tall building. She has just reached 1/3 of the way to the top. She goes 6 more floors up and is now 2/5 of the way to the top. How many floors does the building have?

2) In the following sequence, how many squares are needed to construct the nth figure?
(Express your answer in terms of n)

3) The sum of three integers is 107. The first integer is 1 more than 1/4 of the third. The second integer is 1 less than twice the first. What is the mean of the three integers? Round your answer to the nearest tenth.

4) Sam takes two steps forward and one back, three steps forward and two back, and four steps forward and three back. If Sam repeats this pattern 4 more times (forward and back), how many total steps will Sam have taken?

5) How many integers satisfy the following equation?
    (x + 2) (x - 5) ≤ 0