A 3-sided rectangular pen is being built to hold 15 cows while allowin

ksyed

Each cow needs 30 square feet and we have 15 of them, so we need 450 square feet. We need two dimensions, x and y, such that xy = 450 and x+2y = one of the answer choices. There are a bunch of pairs that we can try for xy = 450 but I think the first one that pops out is 45*10. Wouldn't you know: 45+2(10) = 65 and that's one of our options.

Answer choice D.

I believe the quickest way to the solution is to utilize the answer choices. This is definitely one of those questions put up to expand one’s mind and to give it a good exercise.

15 cows each need 30 square feet of area ——-> 450 square feet of area

Since the length and width must be integers, we are looking for a factor pair that multiplies to 450.

Concept: given a constant product (here length * width = 450), we minimize the addition of those two numbers by making them as close to equal as possible.

Since all the answer choices are relatively small (we don’t have any sums in the ballpark of 1 + 1 + 450 = 452), it would make sense to start at the factor pair closest to the square root of 450 and work backwards.

Key point: we only have 3 sides of fence. Thus, we will be adding one part of the factor pair twice and the other part of the factor pair once.

18 * 25 = 450

18 + 18 + 25 = 61 (not an answer)
Or
18 + 25 + 25 = 68 (not an answer)

15 * 30 = 450

15 + 15 + 30 = 60 (not an answer)
Or
15 + 30 + 30 = 75 (not an answer)


10 * 45 = 450

10 + 10 + 45 = 65 —— BINGO

Answer *D*

Posted from my mobile device