Problems of the Week February 12 to February 16

Feb 12, 2018 | Cambridge

Lower Elementary:
Question: Freddy’s grandfather reads him a story that is 49 pages long. If it takes Freddy’s Grandfather 2 minutes to read each page, then how long will it take to read the story?
Answer: 1 hour 38 minutes
Solution: Since each page takes 2 minutes to read, we can find the total amount of time the story by taking the number of pages and doubling it: 49 + 49 = 98. So, the story will take 98 minutes to read. Since an hour is 60 minutes, the story will take 1 hour and 98 – 60 = 38 minutes.

Upper Elementary:
Question: Westley is 6 feet tall. He can reach objects 20 inches over his head­—24 inches if he stands on his tiptoes. Can Westley reach a pitcher that is hanging 90 inches off the ground?
Answer: Yes
Solution: Since there are 12 inches in a foot, Westley is 6 × 12 = 72 inches tall. He can reach objects 24 inches over his head, so he can reach up to 72 + 24 = 96 inches off the ground. The pitcher is only 90 inches off the ground, so Westley can easily reach it.

Middle School:
Question: The average rat weighs half a pound. A rodent of unusual size weighs 37.5 pounds. What percentage of a rodent of unusual size’s weight does the average rat weigh?
Answer: 1.3%
Solution: To find out what fractional part of 37.5 pounds a 0.5–pound rat is, we divide 0.5 by 37.5 to get 0.11.3. A rat is therefore 1.3% the size of a rodent of unusual size.

Algebra and Up:
Question: Max and Valerie are mixing a magic potion. Max pours 24 ounces of swamp water into the cauldron. Valerie pours 8 ounces of unicorn snot into the cauldron. How many more ounces of swamp water does Max need to add to the cauldron to dilute the mixture to 20% unicorn snot?
Answer: 8 ounces
Solution: Max and Valerie’s potion is 24 + 8 = 32 ounces in total, and 8 ÷ 32 = 25% of the mixture is unicorn snot. In order for the 8 ounces of unicorn snot to be 20% of the x-ounce mixture, 8 ÷ x = 20% and x = 40 ounces. So, since 40 – 32 = 8, 8 ounces of swamp water must be added to dilute the mixture to 20% unicorn snot.

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