Problems of the Week

Jul 3, 2017 | Stone Oak

Problems of the Week! July 3rd

Lower Elementary:Question: Anna picks twice as many tomatoes as Brayden. Catherine picks 12 more tomatoes than Brayden. If Catherine picks 16 tomatoes, then how many tomatoes does Anna pick?

Answer:  8 tomatoes

Solution:  Catherine has 16 tomatoes, so Brayden must have 16 – 12 = 4 tomatoes. Anna has twice as many, so she has 4 × 2 = 8 tomatoes.

Upper Elementary:

Question: Francis is chopping a 10-layered onion. He first cuts the onion in half vertically, from stem to roots. He then cuts each half of the onion 4 times horizontally. How many pieces of onion does Francis have after he separates all the layers?

Answer:  100 pieces

Solution:  There are 10 layers of onion, so we can think of that as 10 pieces. When Francis cuts the onion in half, that makes twice as many pieces: 10 × 2 = 20. When he cuts each half onion horizontally 4 times, he multiplies the number of pieces by 5: 20 × 5 = 100.

Middle School:

Question: John is growing broccoli in his garden. He plants the broccoli in the morning on April 1. 96,480 minutes later, he harvests the broccoli. On what date does John harvest the broccoli? (You may look up how many days are in each month.)

Answer:   June 7

Solution:  If we divide 96,480 minutes by 60 minutes, we find that John harvested the broccoli 1,608 hours after he planted it. 1,608 hours ÷ 24 hours = 67 days. So, John harvested the broccoli on June 7, 67 days after April 1.

Algebra and Up:

Question: A strawberry has 1 seed per 5 square millimeters on its surface. Use the formula for the surface area of a cone—surface area = πr(r+sqrt[h2 + r2])—to approximate the number of seeds on an almost-cone-shaped strawberry whose height is 36 mm and whose diameter at its widest is 54 mm. Round your answer to the nearest whole number.

Answer:  1,221 seeds

Solution: Answers may vary, depending on where in the process you round. Since the diameter of the strawberry is 54 mm, its radius is 27 mm. When we substitute those values into the equation, we find that the surface area of a cone with the same dimensions is 1,944π square millimeters. If we divide that by 5, we get 388.8π, or about 1,221. So, we can approximate that the strawberry has 1,221 seeds.