Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 5 Measurement

Problem
Hint
1) Duane has been collecting quarters for the past few years. He has 98 quarters and has decided to spend his quarter collection on a new movie that costs $10. Duane spends half of his remaining money on lunch. How much money does Duane have left? 1. Compute how many dollars and cents 98 quarters is = _____.
2. Subtract $10 from that = _____.
3. Take half of the remainder = _____.

2) Bart makes 9 liters of fruit punch, which consists of two ingredients: apple juice and cranberry juice. He follows the recipe and mixes together twice as much apple juice as cranberry juice. He and his three friends drink 1 liter of the punch, which Bart then replaces with a liter of cranberry juice. How much apple juice is now in the punch? Express your answer in whole numbers and fractions.
1. If Bart makes 9 liters of punch and there is twice as much apple juice as cranberry juice then the amount of apple juice = _____ liters.
2. This is _____ of the punch.
3. The one liter they drank has ____ liter of apple juice.
4. Subtract this from the original amount of apple juice to get the remaining amount of apple juice = ______ liters.

3) Lila went to a park that was 1 kilometer away from her house. When she left her house, she started riding her bike towards the park and then she walked the rest of the way. Her riding pace was 4 times as fast as her walking pace, but she spent the same amount of time on her bike as she did walking. How far did she ride her bike? Write the answer in meters.
If Lila rode 4 times the walking pace and the same amount of time was spent riding as walking, then she covered ____ of the distance to the park riding = _____ meters.

Problem
Hint
4) Union Middle School has a U made from large square red tiles in the middle of the entry way leading up to the main doors. The width of one tile is 4 feet and each piece of the U is one tile wide - see drawing. The area of the U is 160 square feet. What is its perimeter?. 1. Divide the total area of the U by the area of 1 square tile to get the number of tiles = _____.
2. Using this number of tiles, find how many fit across the bottom of the figure and how many are on each of the vertical sides above the bottom. Bottom = _____ tiles. Each vertical side is ____ tiles.
3. Using these numbers, compute the lengths of each of the sides of the figure and write them in.
4. Add them up. Perimeter = ____ ft.

5) Joey swims 60 laps in a 25 yard pool. One lap is two lengths of the pool. How far did Joey swim in miles, yards, and feet? 1 mile = 5280 ft.
1. Compute the number of yards Joey swims as 60 times the length of one lap (2 lengths of the pool) = _____ yards.
2. Convert this to feet = _____.
3. Convert this to miles = _____.