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18 Jun 2019, 00:41
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45% (medium)

Question Stats:

58% (02:09) correct 42% (02:35) wrong based on 26 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

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John buys koolaid for 12$at a local store. If he bought it at the who [#permalink] ### Show Tags Updated on: 18 Jun 2019, 02:57 Price* quantity= expenditure Only expenditure is given as$12.
Price*quantity=12
Now we look for numbers which when multiplied with another number would result in 12.

Price*quantity=12
1*12=12
2*6=12
3*4=12
4*3=12
6*2=12
12*1=12

Let's take 4*3=12
Price at the local store= $4 & Quantity= 3 liters. If he had bought the item at the wholesaler then he would get extra liter and the price would have been reduced by$1 for $12. Which means that Price at the wholesaler=$3 & quantity=4 liters which would also result in $12. So, the price at the local store is$4.

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Originally posted by Jansaida on 18 Jun 2019, 01:06.
Last edited by Jansaida on 18 Jun 2019, 02:57, edited 2 times in total.
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John buys koolaid for 12$at a local store. If he bought it at the who [#permalink] ### Show Tags 18 Jun 2019, 02:17 Bunuel wrote: John buys koolaid for 12$ 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$cheaper per liter at the wholesale store. what is the price per liter of the koolaid at the local store A. 3 B. 4 C. 5 D. 6 E. 7 L=Liters; Pl=Price at local;Pw=Price at wholesale Local equation : L*Pl=12$; Pl=12/L
Wholesale equations: Pw=(12/L)-1=(12-L)/L; (L+1)*Pw=12$Sub Pw : (L+1)*(12-L)/L=12$;
-L^2+11L+12=12L;
L^2+L-12=0;
(L+4)*(L-3)=0
L=3 So Price is 4$IMO B _________________ Give +1 kudos if this answer helps..!! Director Joined: 20 Jul 2017 Posts: 547 Location: India Concentration: Entrepreneurship, Marketing WE: Education (Education) Re: John buys koolaid for 12$ at a local store. If he bought it at the who  [#permalink]

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19 Jun 2019, 06:14
Bunuel 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

A. 3
B. 4
C. 5
D. 6
E. 7

Let the number of liters bought at a local store = n
and price per liter = p $--> n*p = 12 ....... (1) At wholesale, for 12$, number of liters = n + 1 and the price per liter = (p - 1)
--> (n + 1)*(p - 1) = 12 ....... (2)

To find p, substitute the value of n from (1) in (2)
--> n + 1 = $$\frac{12}{(p - 1)}$$
--> $$\frac{12}{p}$$ + 1 = $$\frac{12}{(p - 1)}$$
--> $$\frac{12}{(p - 1)}$$ - $$\frac{12}{p}$$ = 1

Either cross multiply to get quadratic and solve
Or
Try and substitute the value of p from options

A. 3 --> $$\frac{12}{(p - 1)}$$ - $$\frac{12}{p}$$ = 1
--> $$\frac{12}{(3 - 1)}$$ - $$\frac{12}{3}$$ = 1
--> 6 - 4 = 2 - NO

B. 4 --> $$\frac{12}{(p - 1)}$$ - $$\frac{12}{p}$$ = 1
--> $$\frac{12}{(4 - 1)}$$ - $$\frac{12}{4}$$ = 1
--> 4 - 3 = 1 - YES

IMO Option B

Pls Hit Kudos if you like the solution
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30 Jun 2019, 18:57

Solution

Given:
• 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

To find:
• The price per liter of the koolaid at the local store

Approach and Working Out:
• Let us assume that John buys ‘x’ liters of koolaid at the local store
o So, the cost of 1 liter of koolaid at the local store = $$\frac{12}{x}$$

• At the wholesale store, he would get (x + 1) liters of koolaid for 12$o So, the cost of 1 liter of koolaid at the wholesale store = $$\frac{12}{(x + 1)}$$ • $$\frac{12}{(x + 1)} = \frac{12}{x} – 1$$ o $$\frac{12}{(x + 1)} = \frac{(12 – x)}{x}$$ Simplifying it, we get, o $$12x = 11x – x^2 + 12$$ o $$x^2 + x – 12 = 0$$ o (x + 4) * ( x – 3) = 0 o Thus, x = 3 • Therefore, the price per liter of the koolaid at the local store $$\frac{12}{x} = \frac{12}{3} = 4$$$

Hence, the correct answer is Option B.

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