A certain business produced x rakes each month form November

Question

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

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

Bunuel · Accepted Answer

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.

bharatS · Answer

Hello There,
I hope this helps.

geturdream · Answer

sum of the costs incurred at the beginning of the month
=(1+2+....+7)X/2 * .1 $
=1.4X $

subhashghosh · Answer

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

ashu1983 · Answer

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

amit2k9 · Answer

the costs are = 7x/2 +5x/2+3x/2+x/2+3x+3x+x = 14x 
14x * 0.1 = 1.4x

bellcurve · Answer

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

geometric · Answer

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

shreygupta3192 · Answer

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.

Bunuel · Answer

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

BrainLab · Answer

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

anairamitch1804 · Answer

Please find the solution below in terms of algebra.

DHAR · Answer

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.

ScottTargetTestPrep · Answer

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

almogsr · Answer

it might be too obvious if you say that shipment is in beginning of month and payment later, but still this is the only trick in the question the rest is simple

Noida · Answer

After the first rake is shipped, 7 rakes are left and the storage cost of 7 rakes is 0.7
After this, one more rake is shipped and the storage cost for 6 rakes is 0.6

Therefore, total storage cost = 0.7+0.6+0.5+0.4+0.3+0.2+0.1 = 1.4

siddhantvarma · Answer

I originally thought the same and calculated an answer based on this, only to realise it's not present in any of the options given. So, I simply subtracted the 4x from my answer, assuming that the first month would have no shipments, and therefore the storage cost would apply to the entire inventory. 
When I read the question carefully, nowhere does it say

The first line tells us that each month x/2 rakes were shipped, that's it. We don't know if they were shipped on the first of the month, on the last day of the month, etc.

The second line tells us that a $0.1/rake cost would apply for each month for the rakes not shipped, which is simply total rakes - rakes shipped that month. This tells us this count applies to the rakes that are not shipped that month, so it factors in the rakes that are shipped that month and not the previous month.

Hope this helps!

egmat · Answer

Here's my approach to this inventory and cost tracking problem.

I can see this is testing your ability to systematically track inventory levels over time while calculating cumulative storage costs. Let me walk you through the logical framework that makes this manageable.

The key insight:  You need to think of this as two distinct phases - a production phase with no costs, followed by a shipping phase where inventory decreases monthly while incurring storage costs on remaining stock.

Step 1: Track the Production Phase (Nov-Feb) 
During these 4 months, the business produces  x  rakes each month with no storage costs.
Total inventory entering March =  4x  rakes

Step 2: Set Up the Shipping Phase Pattern (Mar-Oct) 
Here's what happens each month during the 8-month shipping period:
- Start with inventory from previous month
- Ship  \frac{x}{2}  rakes at the beginning of the month 
- Pay $0.10 storage cost for each remaining rake for that entire month

Step 3: Calculate Month-by-Month Storage Costs 
Let me show you the pattern by tracking the first few months:

March: Start with  4x , ship  \frac{x}{2} , store  4x - \frac{x}{2} = \frac{7x}{2}  rakes
Storage cost =  \frac{7x}{2} 	imes 0.10 = 0.35x

April: Start with  \frac{7x}{2} , ship  \frac{x}{2} , store  3x  rakes 
Storage cost =  3x 	imes 0.10 = 0.30x

May: Store  \frac{5x}{2}  rakes, cost =  0.25x

Following this pattern through October and adding all monthly costs:
 0.35x + 0.30x + 0.25x + 0.20x + 0.15x + 0.10x + 0.05x + 0 = 1.40x

Answer: C. 1.40x

Notice how the inventory decreases by  \frac{x}{2}  each month, creating an arithmetic sequence for the storage costs. This systematic tracking approach is crucial for these multi-period business problems.

The complete solution on  Neuron  shows you the systematic framework for tackling all inventory tracking problems, plus an alternative smart numbers approach that makes the arithmetic even cleaner. You can also practice similar multi-step business problems with detailed solutions  here on Neuron  to build consistency with these question types.

A certain business produced x rakes each month form November

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