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A certain business produced x rakes each month form November

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A certain business produced x rakes each month form November  [#permalink]

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New post 26 Sep 2010, 11:38
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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
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Re: Storage Cost  [#permalink]

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New post 26 Sep 2010, 11:42
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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 \(2.8=1.4x\).

Answer: C.
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Re: Storage Cost  [#permalink]

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New post 26 Sep 2010, 20:02
sum of the costs incurred at the beginning of the month
=(1+2+....+7)X/2 * .1 $
=1.4X $
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Re: Storage Cost  [#permalink]

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New post 19 Apr 2011, 19:46
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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

Answer - C
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Re: Storage Cost  [#permalink]

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New post 19 Apr 2011, 20:21
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

Correct Answer C
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Re: Storage Cost  [#permalink]

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New post 26 May 2011, 00:21
the costs are = 7x/2 +5x/2+3x/2+x/2+3x+3x+x = 14x
14x * 0.1 = 1.4x
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Re: Storage Cost  [#permalink]

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New post 26 May 2011, 09:09
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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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New post 05 Nov 2013, 11:55
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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New post 17 Sep 2014, 12:46
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.
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Re: A certain business produced x rakes each month form November  [#permalink]

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New post 17 Sep 2014, 13:14
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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.


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.

Please re-read the question and the solutions above.

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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New post 19 Oct 2014, 19:09
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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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New post 19 Jan 2016, 13:17
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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New post 14 Jan 2017, 14:57
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Please find the solution below in terms of algebra.
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business.PNG [ 11.37 KiB | Viewed 10849 times ]


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Re: A certain business produced x rakes each month form November  [#permalink]

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New post 25 Jul 2017, 08:19
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Explanation:

Given certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October.

From November to February, i.e. in 4 months, x rakes each month are produced.
⇒ Total number of racks produced = 4x

Also given 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.

From March to October, i.e. in 8 months, x/2 rakes each month are shipped. Hence, from March onwards, number of rakes decreases by x/2 at the beginning of every month.

Total storage cost in 12 months
= Storage cost from Nov. to Feb. + storage cost from March to Oct.
= 0 + storage cost from March to Oct.

Number of racks remaining in March = 4x − x/2 = 7x/2. Similarly number of racks remaining from April through September will be 3x, 5x/2, 2x, 3x/2, x and x/2.

Total storage cost from March to Oct. = 0.10 (7x/2 + 3x + 5x/2 + 2x + 3x/2 + x + x/2) = 1.40x

Answer: C.
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Re: A certain business produced x rakes each month form November  [#permalink]

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New post 06 Jun 2019, 18:09
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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


We know that the business didn’t need to pay storage costs from November to February. So let’s begin by analyzing what happened in March. Just before March, the business had 4x rakes, and at the beginning of March, they shipped out x/2 rakes; therefore, for the month of March, they had 4x - x/2 = 8x/2 - x/2 = 7x/2 rakes that required storage costs of $0.10 each.

Since they shipped out x/2 rakes at the beginning of each of the subsequent months, from April to October, the number of rakes in storage in these months are 6x/2, 5x/2, 4x/2, 3x/2, 2x/2, x/2 and 0, respectively. Including the 7x/2 rakes in March, the total number of rakes that require storage costs is:

(7x/2 + 0)/2 * 8 = 7x/2 * 4 = 14x

Since each rake cost $0.10 to store, the total storage costs are 14x * 0.1 = 1.4x dollars.

Answer: C
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Re: A certain business produced x rakes each month form November   [#permalink] 06 Jun 2019, 18:09
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