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# A grocer is storing soap boxes in cartons that measure 25

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Re: Soap boxes in a carton [#permalink]
Zarrolou wrote:
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A -210
B - 252
C - 280
D -300
E-420

Area of the box = $$25*42*60=63000$$
Area of one soap = $$7*6*5=210$$
Tot number = $$\frac{63000}{210}=300$$

You have to calculate the area of the box, then divide it by the area of one soap, and you ll find the number of soaps that will fit into the box
D

I am getting confused between volume approach as done by you and my thought process:

Think about lining up the dimensions of the small boxes along the dimensions of the carton so that you can fill the carton with no wasted space. Since one edge of the small box is 7 inches, that edge of the small boxes should be placed along the side of the carton that is 42 inches long, since 42 is the only dimension that can be divided by 7 evenly. Thus you can put six small boxes along that side, but if you do that 6*6 soap boxes will have width 36 which would be greater than 25 & will exceed the carton width. so how can we just divide the volume of the carton & the soap's volume.

Or am I thinking too much ??
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Re: Soap boxes in a carton [#permalink]
I guess you are thinking too muck
For example you say:
"Since one edge of the small box is 7 inches, that edge of the small boxes should be placed along the side of the carton that is 42 inches long, since 42 is the only dimension that can be divided by 7 evenly."
Are you sure? I mean, what you say isn't wrong, but is not correct either (if we want to answer this particular question). On a side of 42 you can place 6 soaps on their "7-side"(6*7=42) or 2 soaps on their "6-side" and 6 soaps on their "5 side"(6*2+6*5=42). You can also rotate those soaps...
The correct approach is also the simplest in this case.

Hope it's clear
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
The answer works in this case... what if the dimension of the soap box was 6 7 8... This approach would fail then?
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
I'm not convinced... need some experts to help here....

I think the final answer should also include some sort of surface area calculations as well.

Hear my logic out

you have a box which is 42 60 25.. The best way to fit the soap box is 7 6 8

So you are going to have an array of 42/7=6 by 60/6=10 = 60 boxes

Now in 25 8 can only go 3 times

So total no of boxes that can be filled is 60x3=180
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
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Much easier if we use fraction:

25*42*60/5*7*6=5*6*10=300

D
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]

$$\frac{25*42*60}{5*7*6} = 5*6*10 = 300$$
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
Hi all,

Cartoon LBH = 25 * 42 * 60

Box LBH = 5 * 7 * 6

One layer of boxes in cartoon = (5*2)*(4*2) = 80
For H of 60, we can have 10 such layers. Hence # of boxes = 800

TO
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
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Hi thorinoakenshield,

To maximize the number of boxes that we can put in this carton, we have to use as much of (if not all of) the space in the carton. Thus, we have to "orient" the boxes in such a way that we use up all of the space in the carton.

The carton's dimensions are 25 x 42 x 60 and each box has dimensions of 5 x 6 x 7

To maximize the number of boxes, I'm going to "line up" the 5 with the 25 and the 7 with the 42.

25/5 = 5 and 42/7 = 6, so the "bottom layer" of boxes will be 30 boxes.

Now the 6 will "line up" with the 60. 60/6 = 10, so we'll have 10 layers of 30 boxes...and all of carton will be completely full.

(10)(30) = 300 boxes.

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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
thorinoakenshield wrote:
Hi all,

Cartoon LBH = 25 * 42 * 60

Box LBH = 5 * 7 * 6

One layer of boxes in cartoon [color=#ff0000]= (5*2)*(4*2) = 80

For H of 60, we can have 10 such layers. Hence # of boxes = 800

TO[/color]

As shown in my earlier post, you just have to divide the Carton LBH by box LBH

$$= \frac{25}{5} * \frac{42}{7} * \frac{60}{6} = 5*6*10 = 300$$
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =25*42*60
Dimensions of the soap = 5*6*7
placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60
we get = 5x6x10 = 300
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
Zarrolou wrote:
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A -210
B - 252
C - 280
D -300
E-420

Area of the box = $$25*42*60=63000$$
Area of one soap = $$7*6*5=210$$
Tot number = $$\frac{63000}{210}=300$$

You have to calculate the area of the box, then divide it by the area of one soap, and you ll find the number of soaps that will fit into the box
D

I would just like to comment that in this case this appproach works fine, but in the case that the boxes weren't proportional to the container it would not be as simple as dividing the total volume of the container by the volume of each box. One would have to maximize the boxes that can fit in every direction and then multiply those.
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
deepri0812 wrote:
A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?

A. 210
B. 252
C. 280
D. 300
E. 420

First, we must make sure that soap boxes can be placed in a carton without any empty space between the soap boxes. Since 25 is a multiple of 5, 60 is a multiple of 6 and 42 is a multiple of 7; it is possible to position the soap boxes in the carton without any empty space.

Now that we know the soap boxes can be placed without any space, we can simply divide the volume of a carton by the volume of a soap box to find the maximum number of soap boxes that can be contained in a carton. The maximum number of soap boxes that can be placed in each carton is:

(25 x 42 x 60)/(7 x 6 x 5) = 5 x 6 x 10 = 300

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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
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Re: A grocer is storing soap boxes in cartons that measure 25 [#permalink]
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