Problems of the Week – January 21 to January 25

Click here ^[1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here ^[2] for an MS Word version of the Problems of the Week.
Click here ^[3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here ^[4] for a Canadian MS Word version of the Problems of the Week.

^[5]Lower Elementary:
Question: A baby saltwater crocodile hatches from its egg with black stripes. After 48 months, the stripes disappear. How many years old is the crocodile when it loses its stripes?
Answer: 4 years
Solution: There are 12 months in a year. Since 12 + 12 + 12 + 12 = 48, the crocodile is 4 years old when it loses its stripes.

^[6]Upper Elementary:
Question: A platypus eats ³/₄ of a pound of worms each day. If a platypus has eaten 3 ounces of worms, what fractional part of its daily worm intake has it consumed?
Answer: ¹/₄
Solution: There are 16 ounces in a pound. Since the platypus eats ³/₄ of a pound of worms each day, that means it eats ³/₄ of 16 ounces = 12 ounces of worms each day. If the platypus has eaten 3 ounces so far, it has eaten ¹/₄ of its daily intake of worms because 3 is ¹/₄ of 12.

^[7]Middle School:
Question: When a baby kangaroo is born, it’s only 2 centimeters long from snout to tail. An adult kangaroo is 2¹/₂ meters long. What percentage of the adult kangaroo’s length is the baby kangaroo?
Answer: ⁴/₅%
Solution: Before we solve this problem, we need to know that there are 100 centimeters in a meter, so the adult kangaroo is 250 centimeters long. One way to solve this problem is to set up a proportion. As a fraction, the baby kangaroo’s length is ²/₂₅₀ of the length of the adult kangaroo. To turn this fraction into a percentage, we can find an equivalent fraction out of 100 because percent means “for each hundred.” Since 100 is ²/₅ of 250, we can multiply both the numerator and the denominator by ²/₅ to get our percentage: the baby kangaroo is ⁴/₅% the length of the adult kangaroo.

^[8]Algebra and Up:
Question: Koalas have very small brains. An adult koala that weighs 20 pounds has a brain that weighs ³/₄ of an ounce. A typical human brain-to-body weight ratio is 1:40. What is the koala’s brain-to-body weight ratio? How does the koala’s brain-to-body ratio compare to the human’s as a fraction?
Answer: The koala’s brain-to-body weight ratio is 3:1,280, ³/₃₂ of a human’s brain-to-body weight ratio.
Solution: The koala weighs 20 × 16 = 320 ounces, so its brain-to-body weight ratio is ³/₄:320 = 3:1,280. We can rewrite ratios as fractions, so to solve this problem, we need to find what fractional part ³/_1,280 is of ¹/₄₀. To do this, we can solve ¹/₄₀x = ³/_1,280 and find that x = ³/₃₂. So, the koala’s brain-to-body weight ratio is ³/₃₂ of a human’s brain-to-body weight ratio.