A certain business produced x rakes each month form November : GMAT Problem Solving (PS)
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# A certain business produced x rakes each month form November

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26 Sep 2010, 10:38
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A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October? A. 0.40x B. 1.20x C. 1.40x D. 1.60x E. 3.20x [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 36621 Followers: 7103 Kudos [?]: 93601 [7] , given: 10582 Re: Storage Cost [#permalink] ### Show Tags 26 Sep 2010, 10:42 7 This post received KUDOS Expert's post 4 This post was BOOKMARKED udaymathapati wrote: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of$0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
A. 0.40x
B. 1.20x
C. 1.40x
D. 1.60x
E. 3.20x

Pick some smart number for $$x$$, let $$x=2$$ (I chose $$x=2$$ as in this case monthly shipments would be $$\frac{x}{2}=1$$).

From November to February $$4x=8$$ rakes were produced and in March business paid for storage of 8-1=7 rakes, in next month for storage of 6 and so on.

So total storage cost would be: $$0.1(7+6+5+4+3+2+1)=2.8$$ --> as $$x=2$$, then $$2.8=1.4x$$.

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26 Sep 2010, 19:02
sum of the costs incurred at the beginning of the month
=(1+2+....+7)X/2 * .1 $=1.4X$
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19 Apr 2011, 18:46
x + x + x + x -> rakes produced

x/2 * 8 -> Rakes exported

Storage cost =

7x/2 * 0.1 + 3x + 0.1 + 5x/2 * 0.1 + 2x * 0.1 + 3x/2 * 0.1 + x * 0.1 + x/2 * 0.1

( 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5)x * 0.1

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19 Apr 2011, 19:21
Total Rakes produced = 4 months *x
Total Rakes sold each month March - OCt = x/2
Storage cost (3.5 + 3+ 2.5+2+1.5+1+0.5) x * 0.1

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25 May 2011, 23:21
the costs are = 7x/2 +5x/2+3x/2+x/2+3x+3x+x = 14x
14x * 0.1 = 1.4x
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26 May 2011, 08:09
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Total rakes produced 4x.

Rakes in the storage first month 3.5x
Rakes in the storage in the last month 0.5x
Average rakes in the storage 2x
Number of months rakes are in the storage 7 (There are no rakes in the storage in Oct)

so 2x * 0.1 * 8 = 1.4x
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Re: A certain business produced x rakes each month form November [#permalink]

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05 Nov 2013, 10:55
Picking smart numbers is an easy and smart solution here. Here's algebra as well:

4x rakes are produced, x/2 are sold each month, and we're assuming at the beginning of each month.

So storage costs
= .1((4x-x/2)+(4x-2x/2)+(4x-3x/2)+(4x-4x/2)+(4x-5x/2)+(4x-6x/2)+(4x-7x/2)+(4x-8x/2))
= .1(8*4x-36x/2)
= .1(32x-18x)
= .1(14x)
= 1.4x
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Re: A certain business produced x rakes each month form November [#permalink]

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17 Sep 2014, 11:46
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can any one please explain this problem piece by piece..didnt get a single word of this question..
n why r u doing 8-1=7..

kindly explain this
thanku.
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Re: A certain business produced x rakes each month form November [#permalink]

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17 Sep 2014, 12:14
shreygupta3192 wrote:
can any one please explain this problem piece by piece..didnt get a single word of this question..
n why r u doing 8-1=7..

kindly explain this
thanku.

Let $$x=2$$:

The business produced x rakes each month from November through February --> from November to February $$4x=8$$ rakes were produced.
The business shipped x/2 rakes, so 1 rake, at the beginning of March and started paying storage costs in March, so in March business paid for storage of 8-1=7 rakes.

Similar question to practice: the-acme-company-manufactured-x-brooms-per-month-from-januar-144318.html
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Re: A certain business produced x rakes each month form November [#permalink]

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19 Oct 2014, 18:09
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shreygupta3192 wrote:
can any one please explain this problem piece by piece..didn`t get a single word of this question..
n why r u doing 8-1=7..

kindly explain this
thanku.

Hello There,
I hope this helps.
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Re: A certain business produced x rakes each month form November [#permalink]

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01 Jan 2016, 17:19
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Re: A certain business produced x rakes each month form November [#permalink]

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19 Jan 2016, 12:17
udaymathapati wrote:
A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of \$0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?

A. 0.40x
B. 1.20x
C. 1.40x
D. 1.60x
E. 3.20x

You can solve this one using 3 Methods

Method 1
Number picking (see Bunuel's approach)

Method 2
Brute force; Just list the number of monats shipments etc.

Month......1.....2....3........4......5......6.......7.....8
Storage...3,5...3....2,5.....2.....1,5....1......0,5...0 Rakes
Costs....0,35..0,3...0,25..0,2...0,15..0,1...0,05..0 --> 1,4x

Method 3
Number of terms * Average = 7*2=14
14*0,1=1,4
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Re: A certain business produced x rakes each month form November [#permalink]

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14 Jan 2017, 13:57
Please find the solution below in terms of algebra.
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business.PNG [ 11.37 KiB | Viewed 242 times ]

business.PNG [ 11.37 KiB | Viewed 242 times ]

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Re: A certain business produced x rakes each month form November   [#permalink] 14 Jan 2017, 13:57
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