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A certain bakery ran a promotion code: a customer can buy x

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A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 04 Apr 2012, 04:47
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Difficulty:

  65% (hard)

Question Stats:

64% (02:57) correct 36% (02:55) wrong based on 191 sessions

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A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30
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Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 04 Apr 2012, 05:07
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BN1989 wrote:
A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30


The promotion price per donut is \(\frac{15}{x+3}\), thus the promotion price per dozen is \(12*\frac{15}{x+3}\);

The regular price per donut is \(\frac{15}{x}\), thus the regular price per dozen is \(12*\frac{15}{x}\);

We are told that the promotion price per dozen is $2 less than the normal donut price per dozen: \(12*\frac{15}{x+3}+2=12*\frac{15}{x}\) --> \(\frac{180}{x+3}+2=\frac{180}{x}\).

At this point it's better to substitute the values rather than solve for x. Answer choice A, 15, works.

Answer: A.
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Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 15 Jan 2013, 19:42
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BN1989 wrote:
A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30


Responding to a pm:

The wording of the question is such that it is normal to read it twice to understand it well.

Promotion Code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free

This tells us two things:
The regular price of x donuts is $15. So regular price per donut is 15/x
In the promotion, you get 3 donuts free with x donuts. So promotion price per donut is 15/(x+3)

For a dozen, the promotion price is $2 less. So per donut, the promotion price is $2/12 less.

15/x - 2/12 = 15/(x+3)

Now try to plug in values of x from the options.
The equation holds if x = 15

If you face problems making equations in word problems, the issue is practice. You might struggle with 50 advanced word problem questions but then, when you go on to question no. 51, the equation will be more intuitive. Also, don't give up too soon while trying to solve a question (not talking about the actual or simulated tests here). Put in a good 10-15 mins to figure it out on your own before you finally give up and check out the solution. If you are able to solve it on your own, it will give you insight you will never forget.
To practice advanced word problems, you can check out the Veritas advanced word problems book. It will certainly help you get a handle on such questions.
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Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 25 Feb 2014, 16:49
should have plugged in (as per the above advice)...

12[[(15/(X+3)]-[15/x]]=2
...
x^2+3x-270=0
...after doing a prime factorization of 270....
(x-15)(x+18)=0
x=15
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Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 01 Jul 2018, 09:54
BN1989 wrote:
A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30


Regular price of "\(x\)" Donuts is $15, hence regular price of a dozen donuts = \(\frac{(15 *12)}{x}\)

During promotion, 3 donuts are given free for \(x\) donuts at a price of $15, hence it is cost of \((x+3)\) donuts.

Cost of dozen donuts during promotion = \(\frac{(15*12)}{(x+3)}\)

Given that \(\frac{(15*12)}{(x+3)}\) = \(\frac{(15 *12)}{x}\) \(- 2\)

Solving or plugging the answer choices, above we get, \(x = 15\)

Answer A.


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Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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New post 04 Jul 2018, 18:23
BN1989 wrote:
A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30


For the regular price, each donut costs 15/x, and thus a dozen donuts will cost 15/x * 12 = 180/x. For the promotional price, each donut costs 15/(x + 3) and thus a dozen will cost 15/(x + 3) * 12 = 180/(x + 3). Since the promotional price per dozen is $2 less than the regular price per dozen, we have:

180/(x + 3) + 2 = 180/x

Multiplying both sides by x(x + 3), we have:

180x + 2x(x + 3) = 180(x + 3)

180x + 2x^2 + 6x = 180x + 540

2x^2 + 6x - 540 = 0

x^2 + 3x - 270 = 0

(x + 18)(x - 15) = 0

x = -18 or x = 15

Since x can’t be negative, x = 15.

Answer: A
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Re: A certain bakery ran a promotion code: a customer can buy x &nbs [#permalink] 04 Jul 2018, 18:23
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