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John buys koolaid for 12$ at a local store. If he bought it at the who

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Director
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John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 10:09
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Difficulty:

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Question Stats:

57% (01:46) correct 43% (02:00) wrong based on 83 sessions

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John buys koolaid for 12$ at a local store. If he bought it at the wholesale store he would get an extra liter of koolaid for the same cost. Also the koolaid is 1$ cheaper per liter at the wholesale store. what is the price per liter of the koolaid at the local store

A. 3
B. 4
C. 5
D. 6
E. 7
[Reveal] Spoiler: OA

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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 10:36
rxs0005 wrote:
John buys koolaid for 12$ at a local store. If he bought it at the wholesale store he would get an extra liter of koolaid for the same cost. Also the koolaid is 1$ cheaper per liter at the wholesale store. what is the price per liter of the koolaid at the local store

3

4

5

6

7


Let's say John bought x litres of koolaid from the local store.
x liters-> $12
1 liter -> 12/x

Wholesale store:
(x+1) liters -> $12
1 liter -> 12/(x+1)

12/(x+1) is $1 less than 12/x

\(\frac{12}{x+1}+1=\frac{12}{x}\)

\(\frac{13+x}{x+1}=\frac{12}{x}\)

\(13x+x^2=12x+12\)
\(x^2+x-12=0\)
\(x^2+4x-3x-12=0\)
\(x(x+4)-3(x+4)=0\)
\((x-3)(x+4)=0\)

\(x=3 \hspace{2} OR \hspace{2} x=-4\)
Quantity of koolaid can't be negative.
\(x=3\)
John bought 3 liters of koolaid from the local store for $12
Price per liter = 12/x = 12/3 = $4

Ans: "B"
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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 10:53
1
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at local store:
number of liters bought = x
price = p

xp = 12

and wholesale store:
number of liters bought = x + 1
price = p - 1

and (x+1)(p-1) = 12 = xp
solving

x= p - 1

xp = 12 = p*(p-1)

p = 4

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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 11:40
i love the number 12. whenevr there is a question on factors and equality-3 or 4 is the correct answer most of the times. other examples talk abt cost of one being 25% more/less etc.

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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 18:40
p*v = 12 (At local store)

(p-1)(v+1) = 12

So p = 4, by plugging numbers from the choices.

Answer - B
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Director
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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 06 Apr 2011, 19:50
12/(x+1) = 12/x -1

=>x = -4 or 3

=> x = 3 as price cannot be negative.

=> price per liter at local store = 12/3 = 4

Answer B.

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Senior Manager
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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 18 Oct 2016, 16:09
You can solve by deriving the following equation(s) from the prompt:

(1) 12/x=y
(2) 12/(x+1) = y-1

(x+1)(y-1) = 12
xy-x+y-1 = 12
12-x+y=13
-x+y=1 --> y = 1+x

Plug this relationship back into (1) & solve --> You will eventually be faced with x^2 -x-12 = 0 --> x = 4 or -3

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Re: John buys koolaid for 12$ at a local store. If he bought it at the who [#permalink]

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New post 03 Dec 2017, 21:28
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Re: John buys koolaid for 12$ at a local store. If he bought it at the who   [#permalink] 03 Dec 2017, 21:28
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