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n2739178
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Jeff Sackman strange explanation about simplification 22 May 2011, 07:53
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Hi all, I have a question about the way this problem was solved (this is a Jeff Sackmann problem) - see the post after this one...

11. A certain playground has 9 sandboxes, 6 of which require 11 1/6 cubic feet of sand to …fill, and 3 of which require 9 2/3 cubic feet of sand to fi…ll. What is the average amount of sand needed to fi…ll one of the 9 sandboxes?
(A) 10
(B) 10 1/6
(C) 10 5/12
(D) 10 2/3
(E) 11



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Jeff Sackman strange explanation about simplification 22 May 2011, 07:55
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Hi all the explanation is attached in the file in a screenshot.

Can someone please explain why he subtracted 9 2/3 and how that worked?

thanks
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Jeff Sackman strange explanation about simplification 22 May 2011, 09:45
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You better learn the concept and solve normally.

average = {6* (67/6) + 3*(29/3) }/9 = 96/9 = 32/3 => D
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Jeff Sackman strange explanation about simplification 22 May 2011, 13:53
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thanks I know the concept but I don't know why he solved it the way he did (i.e. by subtracting 9 2/3 from each term in the numerator) ... ?
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Jeff Sackman strange explanation about simplification 22 May 2011, 14:53
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n2739178
thanks I know the concept but I don't know why he solved it the way he did (i.e. by subtracting 9 2/3 from each term in the numerator) ... ?
Show more

I am currently working through the problems in Total GMAT math and one of the methods Jeff Sackman advocates for solving weighted averages problems is to subtract the lowest number, then perform the weighted average calculation and then at the very end add back the subtracted value.

E.g: Karen purchases 3 eggs for $17 and 7 eggs for $23. What is the average price Karen paid for each egg?

Ans: Instead of [(3)(17) + (7)(23)]/10 = (51+161)/10 = 212/10 = 21.2

he advocates using -

[(3)(17) + (7)(23)]/10

subtract 17 from both terms =

[(3)(0) + (7)(6)]/10 = 42/10 = 4.2

Now add back 17 = 4.2 + 17 = 21.2

The second method is much faster that calculating (3)(17) = 51 and (7)(23) = 161.

This should be used on a case to case basis.



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