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Jul 15, 2020

# Introduction

This week’s word problems offer a sneak peek into the home of an unusual, magical family — and give your child practice calculating duration, length, weight and volume.

Read this week’s description with your child and choose the word problem that’s the right skill level for them and have them give it a try! After they feel they’ve found the answer, have a look at the solutions!

# An Unusual Home

As Freddy’s grandfather reads him a fantastical story, his uncles Westley, Max, and aunt Valerie work in the cellar on a magic potion! Solve this week’s word problems to get a peek into the home of this unusual family.

Pick the word problem below that’s the right skill level for you. Take your time working it out. When you feel you’ve found the answer, check your solution against ours. No peeking, and have fun!

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?

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?

Middle School:
Question: The average rat weighs half a pound. A rodent of unusual size weighs 37 ½ pounds. What percentage of a rodent of unusual size’s weight does the average rat weigh?

High School 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?

# Solutions

Lower Elementary:
Answer: 98 minutes or 1 hour and 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:
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:
Solution: To find out what fractional part of 3712 pounds a 12–pound rat is, we divide 12 by 3712. To do that, we’d multiply by the reciprocal: 12 × 275 = 175. Since a percentage is out of 100, we multiply both the numerator and the denominator by 113 to get 113 out of 100. A rat is therefore 113% the size of a rodent of unusual size.

Algebra and Up:

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 mixture, 8x = 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.

## OUR METHOD WORKS

Mathnasium meets your child where they are and helps them with the customized program they need, for any level of mathematics.