Problems of the Week: January 13-17

Jan 16, 2020 | North Alpharetta

Each week, Mathnasium publishes math problems to be completed by students. We give students time to work on these during their sessions, as the problems are posted in the center. Below are the problems for the week of January 13-17: ask your students about the problem that best fits their math level! Can they solve it? (Solutions are attached below their respective problems)


Lower Elementary:
Question: Alex has twice as much money as her brother. She spends $3 to buy some trading cards. If her brother has $16, how much money does Alex have after buying the trading cards?
Answer: $29
Solution: If Alex has twice as much as her brother and her brother has $16, then Alex has $16 + $16 = $32. After Alex spends $3 on trading cards, she has $32 – $3 = $29.

Upper Elementary:
Question: Anna, Brayden, and Caleb have three equally sized pies. Anna ate four fifths of her pie. Brayden ate eight ninths of his pie. Caleb ate nine tenths of his pie. Who has the most pie left over?
Answer: Anna
Solution: Notice that the numerator in each fraction is one less than the denominator. That means we can solve this problem by thinking of the denomination as the size of the slices; each person ate all but one slice. Since fifths are bigger than ninths and ninths are bigger than tenths, that means that the person with a fifth of a pie—Anna—has the most left over.

Middle School:
Question: For the first six days of the week, Zelda posted three pictures per day on social media. How many does she need to post on the seventh day to have an average of four pictures posted per day for the whole week?
Answer: 10 pictures
Solution: Zelda posted one less than the desired average on each of the first six days. That means that to have an average of four per day, Zelda will have to post one picture for each day that was one short, and then four more for the last day: 6 + 4 = 10 pictures. Another way to solve this is find that Zelda will need a total of 28 pictures because 28 ÷ 7 = 4. So far, she has 3 × 6 = 18, so she needs 10 more.

Algebra and Up:
Question: A geography teacher has two globes in his classroom. The larger one has a volume of 972π cubic inches. If the ratio between their radii is 3:2, what is the radius of the smaller globe? You may use a calculator to solve this problem.
Answer: 6 inches
Solution: We can solve this problem by finding the radius of the larger globe and then using the ratio between the radii to find the radius of the smaller globe. The volume of a sphere is V = 4/3πr3.
972π = 4/3πr3
972 = 4/3r3
729 = r3
9 = r. The radius of the larger sphere is 9 inches. The ratio between the radii is 3:2. So the radius of the smaller globe must be 6 inches since 9:6 = 3:2.

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