Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Measurement
Problem
Hint
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 ________ sq. ft.
  2. The area of the second room's walls is ________ sq. ft.
  3. Compute the amount of time it takes to paint 1 square foot:= _______ hour to paint 1 square foot.
  4. Compute the amount of time it takes to paint the second room:
    _______ hours.
  5. Divide this by the number of painters to get the time it takes to paint the second room: ________ hours.

2) If May 2nd 2015 is a Saturday, what day of the week will August 23rd, 2016, fall on?
  1. Add the year = _____ days
    (2016 is a leap year)
  2. May = ___ days
  3. June + July = ____ days
  4. August = ____
  5. Total = ____ days
  6. Divide by 7 to get the number of weeks and find the remainder: _____ weeks + _____ days
  7. August 23rd falls on a _________

Problem
Hint

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:
      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:
        _____ inches of twine
  3. The twine to wrap 800 packages is:
        ______ ft.
  4. The number of rolls is _______ 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:
        = _____ per battery
  2. Compute the amount Radio Hut sells 1 battery for:
        = ______ per battery
  3. The profit per battery is ______
  4. The number of batteries they would need to sell is:
        ________ 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.
The radius of the Large pizza is _____ and
The radius of the Extra large pizza is _____
  1. Area of Large pizza = ____________
  2. Area of Extra Large pizza = ____________________
  3. The ratio of the Extra Large area to the Large is:
    _________________