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A clothing manufacturer has determined that she can sell 100

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A clothing manufacturer has determined that she can sell 100 [#permalink] New post 30 Jun 2008, 22:33
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of $200 each. For each rise of $4 in the selling price she will sell two less suits each week. If she sells the suits for x dollars each, how many dollars a week will she receive from sales of the suits?
(A) {(x)(x)} / 2
(B) 200 - (x / 2)
(C) 50x + {(x)(x) / 4}
(D) 150x - {(x)(x) / 4}
(E) 200x - {(x)(x) / 4}

OA and explanation to follow later.
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Re: Clothing Jumbled Up [#permalink] New post 30 Jun 2008, 22:55
100 suits for $200 each

if the price is say x=200+4n they can sell 100-n suits

[ wrong calculation deleted ...]
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Last edited by code19 on 01 Jul 2008, 03:02, edited 1 time in total.
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 01:20
code19 wrote:
if the price is say x=200+4n they can sell 100-n suits

It says "For each rise of $4 in the selling price she will sell two less suits each week", so I guess that they would sell 100-2n suits...

This would lead with the same reasoning that you had to 100 - 2*(x/4-50) = 200x - x^2/2

And that's not an answer choice... I don't get it.


I arrived to the same results another way:

if f(x) is the number of suits they can sell at price x per week, we have f(200) = 100 and f(204) = 98

The equation of f(x), which is a straight line, would be f(x) = 200 - x/2

The amount of dollars they will receive per week is x*f(x), that is 200x - x^2/2

Why is it not an answer choice ??
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 03:01
code19 wrote:
(D)


100 suits for $200 each

if the price is say x=200+4n they can sell 100-n suits

so the return is
(100-n) (200+4n)

however we need to find the solution in terms of x

200+4n = x
n= x/4 - 50

if we put n in the equation (100-n) (200+4n) (for total earning)
the total return is 150x - {(x)(x) / 4}


Oh yes..
Thanks for the correction

So i will do the same calculations with (100-2n)

so the return is
(100-2n) (200+4n) = 8(50-n)(50+n) = 8 (2500 - (n)(n))

however we need to find the solution in terms of x

200+4n = x
n= (x - 200)/4

if we put n in the equation 8 (2500 - (n)(n)) (for total earning)

= 8 (2500 - (x-200)(x-200)/16)
= 200x-(x)(x)/2

The same..
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 04:11
I also got the answer of (200x-1/2x^2). Could anybody clarify this issue pls? Thanks :)
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 05:28
I got 200x-(x^2/4)

For each increase in price of $4 (x-200/4), you have two less suits ->
#suits=100-2*{(x-200)/4}
Double check - $4 increase in price =$204, $204-200=one $4 increment->2 less suits.

So, you have #suits*price=x*[100-{2*(x-200)/4]
=x*[100-{(2x-400)/4}]
=x*[(400-2x+400)/4]
=(400x-2*x^2+400x)/4
=(800x-2*x^2)/4
=200x-(x^2/4)

Sorry for all the parentheses :)
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 05:38
highhopes wrote:
=(800x-2*x^2)/4
=200x-(x^2/4)

Your error is right at the end (the rest is perfectly true): 2*x^2/4 = x^2/2 ;)
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 07:15
abhijit_sen wrote:
OA is E.

Then (E) should be 200x - {(x)(x) / 2} and not 200x - {(x)(x) / 4}
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Re: Clothing Jumbled Up [#permalink] New post 01 Jul 2008, 07:46
Oski wrote:
abhijit_sen wrote:
OA is E.

Then (E) should be 200x - {(x)(x) / 2} and not 200x - {(x)(x) / 4}

I agree this is what I got from old official Full length test. I to initially doubted my calculation but wanted to confirm my findings. :-)
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Re: Clothing Jumbled Up [#permalink] New post 02 Jul 2008, 12:38
abhijit_sen wrote:
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of $200 each. For each rise of $4 in the selling price she will sell two less suits each week. If she sells the suits for x dollars each, how many dollars a week will she receive from sales of the suits?
(A) {(x)(x)} / 2
(B) 200 - (x / 2)
(C) 50x + {(x)(x) / 4}
(D) 150x - {(x)(x) / 4}
(E) 200x - {(x)(x) / 4}

OA and explanation to follow later.


If the answer truly is E, could someone explain what I am doing wrong here. I used actual numbers to find an answer since there are variables in the answer choices.

Initial scenario: 100 suits @ $200 / suit = $20,000 in revenue

Price change: lets say she increased the price by $20 to $220 (x = 220)---> this an increase of $4 -- 5 times. So for every increase of $4 (which is 5), 2 less suits are sold -->
5 * 2 = 10 less suits sold (for a total of 90 suits)

New revenue calculation: 90 suits @ $220 / suit = $19,800 in revenue

Now, lets plus in x (220) for the answer choices to see which answer gives $19,800 as the result:

A) (220*220)/2 = $24,200 --> INCORRECT
B) 200-(220/2) = $90 --> INCORRECT
C) 50(220) + {(220*220)/4} = 23,100 --> INCORRECT
D) 150(220) - {(220*220)/4} = 20,900 --> INCORRECT
E) 200*220 - {(220*220)/4} = 31,900 --> INCORRECT

None of these yield $19,800 ??? :|
I agree with abhijit_sen that E should be 200x - {(x)(x) / 2} ---> which yields $19,800 as the result
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Re: Clothing Jumbled Up   [#permalink] 02 Jul 2008, 12:38
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