Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 7 Measurement
Problem
Solution
1) On April 2, 2013 Mrs Green planted two bushes of the same variety three feet apart, stem to stem. They both have a diameter of 1 foot. The diameter of this kind of bush grows at a rate of 4 inches per year. Assume the growth rate is constant and she doesn't trim the bushes. In what year will the two bushes touch and begin to form a hedge?
  1. If the bushes are planted 3 feet (36 inches) apart and they both have a diameter of 1 foot, then they are separated by 36 - 2x6 = 24 inches.
  2. 24/4 = 6 years = 2019

2) Sarah, Will and Jeff are replacing the fencing at the petting zoo where they work. They need enough fencing to go around the animal pen which is 90 ft by 45 ft. They also need fencing to go around the walkway on the outside of the pen. The walkway is 3 feet wide. If the fencing comes in 12 foot sections, how many sections of fencing will they need to buy to replace all the fencing?
  1. Inner fence: 2x45 + 2x90 = 270 ft
  2. Outer fence: add 6 feet to each dimension to accommodate the walkway:
    2x51 + 2x96 = 294 ft
  3. Total fencing = 564 ft.
  4. Total sections = 564/12 = 47 sections
3) Mr. O'Malley leaves his laptop in Sleep-mode about 10 hours every day when he could actually turn it off according to his son. It uses 1.6 watts per hour of power in Sleep-mode. Electricity costs $0.105 per kilowatt per hour where he lives. A kilowatt is 1000 watts. How much could he save per year if he were to shut his lap top down completely instead of using Sleep mode? Assume there are 365 days in a year. Round to the nearest cent. Sleep mode cost:
10 x 1.6 x 365 x $0.105 = 61.32 cents = 61 cents
        1000

Problem
Solution
4) Geordie finds the blue prints for the apartment building he lives in and can't find the scale. To determine the scale he first measures the length and width of his actual rectangular living room and finds it to be 12 ft by 9 ft. He compares it to the blue print drawing of the living room; it is drawn as a 4 in by 3 in rectangle. He wants to know the area of the luxury apartment's living room 5 floors above his. He measures the blueprint dimensions for the living room of the luxury apartment. It is 7 in by 5 in. What is the area of the luxury apartment's living room?
  1. The scale of the blueprint is
    3 inches = 9 feet, therefore
    1 inch = 3 feet
  2. Area of the luxury apartment's living room =
    (7x3) x (5x3) = 21 x 15 = 315 sq. ft.

5) Chris has a heart shaped cake he wants to share with Sheena and Jess. It is made up of two half circles and a large equilateral triangle with side length 8 inches. It is 1 inch thick all around. The sides are covered with chocolate frosting. The top has vanilla frosting on it. The cake is precut into the four triangles and the two half circles as shown. Sheena wants the two half circle pieces, Jess wants the pieces with the least chocolate frosting, and Chris takes the remaining two pieces. What is the difference in chocolate frosted surface area between Sheena's two pieces and Chris' two pieces? Use pi = 3.14 and round to the nearest tenth.
  1. There are 6 total pieces of cake.
  2. Each person gets 2 pieces.
  3. Sheena's 2 pieces: The diameter of the 2 half-circles is 4 inches so the circumference of the 2 half-circles is 4 inches of chocolate frosting
  4. Jess' pieces: the middle triangle (no frosting) and the upper left triangle piece (4 inches of frosting) = 4 inches of chocolate frosting
  5. Chris' pieces: the bottom triangle
    (2x4 inches of frosting) and the upper right piece
    (4 inches of frosting) = 12 inches of chocolate frosting.
  6. The difference between Sheena's 2 pieces and Chris' 2 pieces is 4 - 12 = 12.56 - 12 = .56 = .6 sq. in.