Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Measurement
Problem
Solution
1) It takes 4 hours for three members of Jo's crew to paint the walls of a square room with a side length of 12 ft and a 10 ft ceiling. How long would it take a crew of five to paint the walls of a square room with a side length of 25 ft and a 12 ft ceiling? (Assume there are no windows and they paint over doors, etc)
  1. The area of the first room's walls is 12x10x4 = 480 sq. ft.
  2. The area of the second room's walls is 25x12x4 = 1200 sq. ft.
  3. Compute the amount of time it takes to paint 1 square foot:
        4x3/480 = 0.025 hour to paint 1 square foot.
  4. Compute the amount of time it takes to paint the second room:
        1200 x 0.025 = 30 hours
  5. Divide this by the number of painters to get the time it takes to paint the second room: 30/5 = 6 hours

2) If May 2nd 2015 is a Saturday, what day of the week will August 23rd, 2016, fall on?
  1. Add the year = May 2nd to May 2nd = 366 days
    (2016 is a leap year)
  2. May = 29 (the 3rd to the 31st)
  3. June + July = 61
  4. August = 23
  5. Total = 366 + 61 + 29 + 23 = 479
  6. 479/7 = 68 + 3 days
  7. August 23rd falls on a Tuesday

Problem
Solution

3) Peter prepares packages measuring 8 in by 10 in by 14 in for shipping. He ties each package as shown in the figure with a continuous length of twine, secured with an efficient knot on top of the package that is 3 in long. If twine comes in 500 ft rolls, how many rolls will he need to prepare 800 packages?
  1. There are 3 sizes of sides of the package:
      8x10, 8x14 and 10x14 and there are 2 of each size
  2. Each face has L + W lengths of twine, so the total amount of twine for one box is:
        2(8+12) + 2(8+14) + 2(10+14) =
        40+44+48 + 3 = 135 inches of twine
  3. The twine to wrap 800 packages is:
        800x135 = 108000 inches = 9000 ft.
  4. The number of rolls is 9000/500 = 18 rolls

4) Radio Hut buys batteries wholesale at a rate of 150 for $45, and sells them in packages of 8 for $5. To make a profit of $195, how many batteries would they need to sell?
  1. Compute the amount Radio Hut pays for 1 battery:
        $45/150 = $0.30 per battery
  2. Compute the amount Radio Hut sells 1 battery for:
        $5/8 = $0.625 per battery
  3. The profit per battery is $0.625 - $0.30 = $0.325
  4. The number of batteries they would need to sell is:
        $195/$0.325 = 600 batteries.

5) Pizza Place's Extra Large pizza has a diameter 50% greater than that of its Large pizza. What is the ratio of the area of the Extra Large pizza to that of the Large pizza? 		Use X for the diameter of the Large pizza.
  1. Area of Large pizza = (X⁄2)2 = (X2⁄4)
  2. Area of Extra Large pizza = (1.5X⁄2) 2 = (2.25X2⁄4)
  3. The ratio of the Extra Large area to the Large is:
        (2.25X2⁄4) / (X2⁄4) = 2.25 : 1