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


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


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 [#permalink]
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A customer can buy x donuts for the regular price of $15 total: Price per donut: \(\frac{15 }{x }\)

In promotion: price per donut: \(\frac{15 }{(x+3) }\)

Promotion price is $2 less per dozen: \(\frac{15 }{x }\) - \(\frac{2 }{12 }\) = \(\frac{15 }{(x + 3) }\)

=> Can substitute the option to get x = 15.

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



Decrease in price per donut=2/12=1/6
At promotion price $15 can buy no. of donuts=(x+3)= 3/1/6=18
Therefore x=18-3=15

Answer A
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Re: A certain bakery ran a promotion code: a customer can buy x [#permalink]
Normal price per 1 donut = $15 / X donuts

Normal price per dozen donuts = (15/X) * 12


Get 3 donuts free for the Same Total of $15

Discount Price per 1 Donut = $15 / (X + 3)

Discount Price per dozen = (15)/(X + 2) * 12


The difference in Prices per Dozen Donuts is $2


(15/X) * 12 - (15)/(X + 2) * 12 = 2

——divide each side of the equation by 12—-



(15/X) - (15)/(X + 2) = 1/6 *******


2 Methods:

(1)can find the LCD and Factor the Quadratic

Or

(2)Plug in Answer Choices for X


-A- 15

X = 15 donuts

(15/15) - (15/18) = 1/6?

1 - (5/6) = 1/6


Correct Answer is -A-

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