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Problems of the Week – February 19 to Febraury 23

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: Mikey and his brothers Donnie, Raph, and Leo are comparing their heights. Leo’s height is between Raph’s and Donnie’s. If Raph is the second shortest, who is the shortest?
Answer: Mikey
Solution: If Raph is the second shortest and Leo’s height is between Raph’s and Donnies, then both Leo and Donnie are taller than Raph. That means that Mikey must be the shortest.

[6]Upper Elementary:
Question: Three-fourths of a cannister of toxic ooze spills into a sewer. If 4½ fluid ounces of ooze is left inside the cannister, then how much ooze does the cannister hold in total?
Answer: 18 fluid ounces
Solution: Since ¾ of the cannister of ooze spilled, that means that 4½ fluid ounces is ¼ of the total amount of ooze the cannister can hold. So, the cannister can hold 4½ × 4 = 18 fluid ounces in total.

[7]Middle School:
Question: April is deciding what kind of job she should take. She’s deciding between jobs as a lab assistant (which will pay her $48.00 for 4 hours of work), a computer programmer (which will pay her $65.00 for 5 hours of work), and a reporter (which will pay her $69.00 for 6 hours of work). Which job should she take if she wants to earn the most money per hour?
Answer: Computer Programmer
Solution: The lab assistant job pays $48.00 ÷ 4 = $12.00 per hour. The computer programmer job pays $65.00 ÷ 5 = $13.00 per hour. The reporter job pays $69.00 ÷ 6 = $11.50 per hour. So, if April wants to earn the most money per hour, she should take the job as a computer programmer.

[8]Algebra and Up:
Question: A 16-inch pizza is cut into 6 equal slices. If 4 consecutive pieces are taken and eaten, then what is the area taken up by the remaining slices?
(Hint: Pizzas are measured by their diameters.)
Answer: 21⅓π square inches
Solution: Before any slices are eaten, the pizza takes up πr2 = 64π square inches. Since 4 out of 6 slices were eaten, that leaves 2 slices, so ⅓ of the pizza is left over. That means that the area taken up by the remaining two slices is ⅓ × 64π = 21⅓π square inches.