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A motorcycle importer is planning on increasing the price of

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A motorcycle importer is planning on increasing the price of [#permalink] New post 04 Jul 2005, 06:33
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A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76
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Re: Word problem [#permalink] New post 04 Jul 2005, 06:51
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rxs0005 wrote:
An importer of bikes is plannig to increase the price of a bike by 1000$.
At this new price 5 fewer bikes will be sold but total revenues will increase by 26000$ to 594000$. What is the number of bikes the manufactuer will seell at thhis new price.

Is there a simpler way to do this i got a quadratic equation.


66 bikes.

Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.

factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.

Hence 66.

HMTG.
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Re: Word problem [#permalink] New post 04 Jul 2005, 10:03
HowManyToGo wrote:
66 bikes.

Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.

factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.

Hence 66.

HMTG.


Can you be more explicit as to how you deduced bikes*price = 568 units from bikes*units=$568000
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Re: Word problem [#permalink] New post 04 Jul 2005, 18:26
rthothad wrote:
HowManyToGo wrote:
66 bikes.

Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.

factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.

Hence 66.

HMTG.


Can you be more explicit as to how you deduced bikes*price = 568 units from bikes*units=$568000


Substituted $1000 as 1 unit.

HMTG.
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Re: Word problem [#permalink] New post 05 Jul 2005, 01:30
HowManyToGo wrote:
rthothad wrote:
HowManyToGo wrote:
66 bikes.

Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.

factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.

Hence 66.

HMTG.


Can you be more explicit as to how you deduced bikes*price = 568 units from bikes*units=$568000


Substituted $1000 as 1 unit.

HMTG.

HMTG, Yes I did follow that, I was more interested in understanding why you did that, how did you know that 1 unit costs $1000.
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Re: Word problem [#permalink] New post 05 Jul 2005, 01:36
rthothad wrote:
HowManyToGo wrote:
rthothad wrote:
HowManyToGo wrote:
66 bikes.

Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.

factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.

Hence 66.

HMTG.


Can you be more explicit as to how you deduced bikes*price = 568 units from bikes*units=$568000


Substituted $1000 as 1 unit.

HMTG.

HMTG, Yes I did follow that, I was more interested in understanding why you did that, how did you know that 1 unit costs $1000.


There is no unit which costs $1000, just that I chose that as 1 unit.
Also I did it to reduce big numbers, you can cancel out 1000 on both sides of the original equations , and get it down to what I used.

HMTG.
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 [#permalink] New post 10 Dec 2006, 15:50
The shortest way I could think of to solve this prob is to set up equations first, then backsolve.

P: the price of each bike before the increase
B: the number of bikes before the increase

Then the change in revenue is
1000(B-5) - 5P = 26000

we also have P*B = 594000 - 26000 = 568 000.

Backsolve starting with B. Since B-5 = 61, 5P = 61 000 - 26 000. P = 7000. PB < 568 000. Eliminate A and B.

Backsolve with D, we will have PB>586000.

Then, C must be the answer
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A motorcycle importer is planning on increasing the price of [#permalink] New post 22 Mar 2014, 05:12
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51

(B) 61

(C) 66

(D) 71

(E) 76

Guys can you help please?

This is how I am trying to solve this, but getting no where.

New revenue = $594,000
Old revenue = $594,000 - $26,000 = $568,000

Where I am struggling is to choose the variables and form the equation. Can someone please help?
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 22 Mar 2014, 12:05
try to think how we calculate revenue, should revenue=unit price*number of items sold
if you assume old price is P, number of items sold is N then here is how it looks like

(P+1000)*(N-5)=594000, also

P*N= 594000-26000

you can solve it from there

when you get N=71, remember that is the previous Number of item, you have to minus 5 to get current
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 23 Mar 2014, 04:55
Expert's post
enigma123 wrote:
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51

(B) 61

(C) 66

(D) 71

(E) 76

Guys can you help please?

This is how I am trying to solve this, but getting no where.

New revenue = $594,000
Old revenue = $594,000 - $26,000 = $568,000

Where I am struggling is to choose the variables and form the equation. Can someone please help?


Merging similar topics.

Please, search before posting. Thank you.


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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 23 Mar 2014, 19:17
Expert's post
(P+1000)(Q-5)=594000
PQ=568000

subtract them and then substitute for P using 2nd equation

200Q-(568000/Q)=6200
Q^2-31Q-2840=0

then just factor, or plug-in keeping in mind that the answer choices will be 5 less than the positive root in the aforementioned quadratic

C
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 26 Apr 2014, 15:19
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Actually its not that tough, one can use backsolving on this one

We have that (q-5)(p+1000)=594,000
We also get that pq=568,000

We are asked for q-5.

Let's look at answer choices

Always start with C

If q-5=66--> q=71

568,000/71=8

Then replace (8000)(71)=568,000

BINGO

Answer: C

Hope this helps
Cheers
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 20 Nov 2014, 20:56
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Hi Bunuel/Karishma - Is there any faster and better way to solve this problem other than plugging in the answer choices in the equations?
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 20 Nov 2014, 22:29
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rxs0005 wrote:
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76


Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:

Assuming x motorcycles were sold every month initially.

(568000/x + 1000)(x-5) = 594000
(568/x + 1)(x-5) = 594

Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 5 = 66 bikes this month

Answer (C)
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 21 Nov 2014, 09:36
Expert's post
VeritasPrepKarishma wrote:
rxs0005 wrote:
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76


Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:

Assuming x motorcycles were sold every month initially.

(568000/x + 1000)(x-5) = 594000
(568/x + 1)(x-5) = 594

Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 5 = 66 bikes this month

Answer (C)


Hi Karishma - The above highlighted part in your reply seems to be the most critical part of this problem and it'd be difficult to get the correct option with ease in such a fashion, I guess, under test environment :-(

I'm assuming there is no other better approach to tackle this sort of problem, just curious whether there is any strategic way to implement this kind of approach in such problems ?

Look forward to your reply.

Thank you!
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Re: A motorcycle importer is planning on increasing the price of [#permalink] New post 07 Dec 2014, 21:52
Expert's post
bagdbmba wrote:
VeritasPrepKarishma wrote:
rxs0005 wrote:
A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?

(A) 51
(B) 61
(C) 66
(D) 71
(E) 76


Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:

Assuming x motorcycles were sold every month initially.

(568000/x + 1000)(x-5) = 594000
(568/x + 1)(x-5) = 594

Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 5 = 66 bikes this month

Answer (C)


Hi Karishma - The above highlighted part in your reply seems to be the most critical part of this problem and it'd be difficult to get the correct option with ease in such a fashion, I guess, under test environment :-(

I'm assuming there is no other better approach to tackle this sort of problem, just curious whether there is any strategic way to implement this kind of approach in such problems ?

Look forward to your reply.

Thank you!


You often get questions involving product of two terms such that one increases and other decreases such that the overall product changes e.g.
Price*Quantity = Revenue
Speed*Time = Distance

In such cases, it is best to make equations and then plug in values.

Also, when dealing with ominous numbers such as 568 and 594, you should know that you cannot calculate taking these numbers in your stride. Hence, you must factor them out and see what you can cancel out or what value of x becomes obvious.
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Re: A motorcycle importer is planning on increasing the price of   [#permalink] 07 Dec 2014, 21:52
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