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

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New post 18 Jun 2019, 00:41
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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]

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New post 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.

IMO the answer is B

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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]

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New post 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
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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 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

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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 21 Jun 2019, 11:55
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 n = the number of liters of koolaid he can buy at the local store and p = the price per liter at the local store. So we have:

np = 12

and

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

Expanding the second equation, we have:

np + p - n - 1 = 12

Since np = 12, we have:

12 + p - n - 1 = 12

p - n - 1 = 0

p = n + 1

Substituting n + 1 for p in the first equation, we have:

n(n + 1) = 12

n^2 + n - 12 = 0

(n + 4)(n - 3) = 0

n = -4 or n = 3

Since n can’t be negative, n = 3, so p = 3 + 1 = 4.

Answer: 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 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.

Answer: B

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Re: John buys koolaid for 12$ at a local store. If he bought it at the who   [#permalink] 30 Jun 2019, 18:57
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