Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Algebra

Problem
1) A TV station uses the following method for determining commercial time for any of its special 2 hour broadcasts. It divides the broadcast into 20 minute segments. In the first 20 minute segment no commercials are aired. Then for each subsequent 20 minute segment the amount of time given to the special is reduced by 25% from the previous 20 minute segment. The remainder of the 20 minutes is given to commercials. In the first hour how much time is spent on commercials to the nearest second?

2) In the following pattern of rectangles, how many squares are needed to make the nth rectangle? Express your answer in terms of n.
3) Rosita wants to take a DVD movie with her on the family vacation. She compares prices. Happy Viewing will give her the DVD for 3 days at $3.00 and then charges $1.50 per day for a late return. Movies-At-Home will give her the DVD for 5 days at $5.00 and charges $1.75 per day for a late return. For how many days can she keep the movie if the total cost to her is the same at both stores? This is the break even day.

Problem
4) Lisa is designing her own house. She draws a side view sketch of the stairs she wants to use to connect the downstairs with the upstairs. She notices there's a line that connects all the edges of the steps as shown in the diagram. If the coordinates giving the edge of the second step are ( 2ft, 3/2ft), what are the coordinates of the edge of the top step?

5) At Emerald Middle School there can be at most 26 students in a class. If Danny's class has twice as many boys as girls what's the biggest his class can be?