Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 6 Measurement

Problem
Solution

1) It costs $50.00 each day to run a small pudding factory. It costs 25 cents to make a pudding cup. How many pudding cups can be made in that day if the factory has $516.00? 		Let N = number of pudding cups
Then N = ($516 - $50)/$0.25
Solve for N = 466/0.25 = 1864 pudding cups
2) Two ice cream men are racing to the park along the same route. Ice cream man Chandler is going 24 meters per minute. Ice cream man Joey is going 3600 centimeters in one minute. Chandler gets to the park in 4 minutes. If they started from the same point, how long will it take Joey to get to the park? Express your answer in minutes and seconds. 1. Convert Joey's rate to meters/minute =
    3600 cm/100 min = 36 m/min
2. Compute the distance Chandler went in 4 minutes =
    24 x 4 = 96 meters.
3. Divide this distance by Joey's rate to get Joey's time =
    96/36 = 2.66667 minutes.
4. Convert this to minutes and seconds = 2 min 40 sec

3) Jordan's backyard is 1300 square feet. She is willing to devote 12% of her yard to a trampoline. What would be the diameter of the largest circular trampoline that would satisfy that? Circular trampolines only come in whole number diameters. Use = 3.14		 1. Compute 12% of the backyard's area =
    .12 x 1300 = 156 sq. ft.
2. Use this area to find the radius of the trampoline =
    3.14 x R2 = 156
    R2 = 156 / 3.14 = 49.68
    R = √49.68 = 7.048
    D = 2 x 7.048 = 14.0968
3. Round down to the next whole foot = 14 ft.

Problem
Solution
4) Rene has a rectangular garden that measures 7 ft by 8 ft. She wants to create a new garden with the same area that will have twice the perimeter, so that she already has half the deer fencing she needs. She also wants the new garden to be narrower so that she can reach across it from either side. What will be the dimensions of her new garden? 1. If she wants to be able to reach across it, the width must be 4 feet or less.
2. Use this guess-and-check table to reduce the width, keeping the area the same and increase the perimeter until it is twice its current value:
WidthLengthPerimeter
41436
318.6743.33
22860
The dimensions are 2 ft. x 28 ft.
5) Kam is playing with a balance. On one side he has a rock. On the other side he has 15 quarters and 10 dimes. The rock side is heavier. When he adds a penny the coin side is heavier. When he takes off a dime the rock side is heavier. A quarter weighs 5.67 grams. A dime weighs 2.268 grams. A penny weighs 2.5 grams. To the nearest tenth of a gram what is the least the rock can weigh and what is the most it can weigh? 1. The most the rock can weigh is the weight of 15 quarters + 10 dimes + 1 penny =
    15 x 5.67 + 10 x 2.268 + 2.5 = 110.23 =
    110.2 grams
2. The least the rock can weigh is the weight of 15 quarters, 9 dimes and 1 penny =
    15 x 5.67 + 9 x 2.268 + 1 x 2.5 = 107.962 =
    108 grams