Problems of the Week – September 24 to September 28

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: On Monday, Magnus carves his very first wooden duck. On Tuesday, he practices by carving 3 more wooden ducks. The next day, he carves 5 more ducks. The day after that, he carves 7 more, and so on. If the pattern continues, on what day of the week will Magnus carve his 20^th wooden duck?
Answer: Friday
Solution: Magnus’s pattern follows the odd numbers. According to the problem, Magnus has 1 + 3 + 5 + 7 = 16 by the end of his carving on Thursday. The next day, Friday, he must carve 9 more ducks. Because 16 + 9 = 25, and 25 is more than 20, he must carve the 20^th duck on Friday.

^[6]Upper Elementary:
Question: Angus is making macarons. His recipe uses 1³/₄ cups of powdered sugar to make a batch of a dozen macarons. If Angus has 3¹/₂ quarts of sugar, how many total macarons can he make?
Answer: 96 macarons
Solution: A quart is equal to 2 pints, or 4 cups. Angus has 3¹/₂ quarts of powdered sugar, which is the same as (3¹/₂ × 4) = (3 × 4) + (¹/₂ × 4) = 12 + 2 = 14 cups. There are 8 groups of 1³/₄ inside of 14, so Angus can make 8 batches with 14 cups of sugar. That would make 8 batches × 12 macarons = 96 macarons.

^[7]Middle School:
Question: Sloane and Jerry are about to race their monster trucks. Sloane’s truck goes 60 miles per hour, while Jerry’s truck only goes 40 miles per hour. Jerry starts his truck as soon as the whistle blows, but Sloane’s engine stalls; and her truck doesn’t start back up until exactly a minute later. At what time after the whistle blows does Sloane catch up with Jerry?
Answer: 3 minutes after the whistle blows
Solution: Sloane’s truck goes 60 ÷ 60 = 1 mile per minute. Jerry’s truck goes 40 ÷ 60 = ²/₃ of a mile per minute. Their distances traveled can be charted.

Minutes after whistle	Sloane	Jerry
1 minute	0 miles	2/3 of a mile
2 minutes	1 mile	11/3 miles
3 minutes	2 miles	2 miles

Sloane catches up to Jerry at the 3 minute mark.

^[8]Algebra and Up:
Question: Lucretia has a giant, cylindrical fish tank. The fish tank has a diameter of 9 feet and is 30 feet tall, including a 2 foot tall metal base which the glass tank sits upon. What is the volume of the fish tank? (Include π in your answer.)
(Hint: volume of a cylinder = πr²h)
Answer: 567π ft³
Solution: The diameter of the tank is 9 ft, so the radius is 4.5 ft. The height of the tank is 30 – 2 = 28 ft. This means that the volume of the tank is π(4.5)(4.5)(28) = 567π ft³.