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

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

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

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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