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Problem of the Week 01-02-2017

Jan 3, 2017

Lower Elementary:

Question: Ellie and Jake have two dogs. Ellie takes one of the dogs on a 38-minute walk. Jake takes the other dog on a walk that takes three-quarters of an hour. If they leave home at the same time, then who will get home again first? By how much?

Answer:  Ellie gets home 7 minutes before Jake.

Solution:  One quarter of an hour is 15 minutes, so three-quarters of an hour is 15 + 15 + 15 = 45 minutes. Since 45 minutes is 45 – 38 = 7 minutes longer than 38 minutes, that means that Ellie gets home again 7 minutes before Jake.

 

Upper Elementary:

Question: Tyler has 8 avocado trees and picks 7 avocados off of each tree. If 4 avocados fit in a box, then how many boxes does Tyler need for all of the avocados he picks?

Answer:  14 boxes

Solution:  Tyler picks 7 avocados, 8 times, which gives him 7 × 8 = 56 avocados. He divides them into groups of 4 to fit in the boxes, so he needs 56 ÷ 4 = 14 boxes for all of the avocados he picked.

 

Middle School:

Question: Peter is 5 feet tall and casts a shadow that is 5'6" in length. His sister Sandra casts a 3'8" shadow. How tall is Sandra?

Answer:  Sandra is 3'4".

Solution:  Each kid and his/her shadow form the legs of similar triangles. Since 5 feet (or 60 inches) must be multiplied by 1.1 to get to 5'6" (or 66 inches), that means that Sandra’s height multiplied by 1.1 is the length of her shadow, 44 inches:

1.1S = 44

S = 40

Sandra is 40 inches tall, or 3'4".

 

Algebra and Up:

Question: If x is an integer, 5x + 2 < 12, and –3 < 2x + 2, then what is the sum of all the possible values of x?

Answer:  –2

Solution:  First, we solve the inequalities:

5x + 2 < 12 ... x < 2

–3 < 2x + 2 ... x > –2.5

So, the possible values of x are –2, –1, 0, and 1 because x is in integer. The sum of its possible values is therefore –2.