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A baker is storing cake boxes in cartons that measure 25 inches by 42 [#permalink]

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20 Nov 2014, 01:20

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A baker is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?

A baker is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?

Re: A baker is storing cake boxes in cartons that measure 25 inches by 42 [#permalink]

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21 Nov 2014, 02:33

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The dimensions of the carton are 25" x 42" x 60" and those of each cake box are 8" x 7" x 5".

To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25" x 42" and fit 5 x 6 boxes of 5" x 7", then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.

Alternatively you could try taking the base as 60" x 42" and fit 12 x 6 boxes of 5" x 7", then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
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Re: A baker is storing cake boxes in cartons that measure 25 inches by 42 [#permalink]

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25 Nov 2014, 22:55

Divide 25/5 to get 5. Well that is one dimension dealt with. Divide 42/ 7 to get 6. another dimension dealt with. Divide the greatest number under 60 by 8(i mean to get an integer). that would be 56. 56/8=7. So 7*5*6= 210. E

Re: A baker is storing cake boxes in cartons that measure 25 inches by 42 [#permalink]

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24 Jan 2015, 13:19

Could you pls explain the reason in adopting a different trick in dealing with this question then the simple one posted in a-grocer-is-storing-soap-boxes-in-cartons-that-measure-150337.html. what is the thing to look for in dealing with these question because on first look both the questions look of the same type...

If you've ever received a package or sent a package that was not completely filled (so extra packaging was included to keep the items in the box from shifting around), then you've experienced what these types of questions are ultimately about: "empty" space.

Since this question asks us to MAXIMIZE the number of boxes that we can put in a carton, we have to think about how to maximize the space given the dimensions of the carton and the dimensions of the boxes that we're going to put into it. Thus, we have to think about MORE than just the volumes. Often, one or more of the wrong answers is based on a conceptual math mistake that might be made, so it's important to take the necessary notes (drawing pictures sometimes helps too) and PROVE that your answer is the correct one.

Here, the issue is about "orienting" the boxes so that we can fill as much of the carton as possible (and minimize the "empty" space.

Re: A baker is storing cake boxes in cartons that measure 25 inches by 42 [#permalink]

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25 Apr 2016, 05:12

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