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P Pencils -> 2q dollar

Convert the dollar into cents

P Pencils -> 200q cents

1 Pencil -> 200q/p cents

In C cents how many pencil -> Total Amount/Amount of 1 item

Total Amount = C
Amount of 1 item = 200q/p

So C/(200Q/P) = CP/200Q
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Quote:
If \(p\) pencils cost \(2q\) dollars, how many pencils can you buy for \(c\) cents? (Tip: 1 dollar = 100 cents)

(A) \(\frac{pc}{2q}\)

(B) \(\frac{pc}{200q}\)

(C) \(\frac{50pc}{q}\)

(D) \(\frac{2pq}{c}\)

(E) \(200pcq\)

Price of a pencil in cents: \(\frac{2q}{p}*100 = \frac{200q}{p}\)
The number of pencils you can buy for c cent:
\(c:\frac{200q}{p} = c*\frac{p}{200q} = \frac{pc}{200q}\)

=> IMO B
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First, 2q dollar = 200q cents
I usually use by a simple matrix:

p pencils = 200q cents
X pencils = c cents

=> p/X = 200q/c
=> X = p*c/200q
=> Answer B
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2q dollars = 200q cents
In 200q cents we get p pencils. So, how many pencils will we get in c cents?
i.e. 200q => p
c => ? Let this be x

Cross multiplying, we get pc = 200qx
Thus, x=pc/200q

Thus, the answer is B.

The focus here should not be on finding the price of one pencil or even how many pencils we can get in 1 dollar or 1 cent but rather on how many pencils we can get in c cents. Focusing on exactly what is asked will allow you to save previous few seconds!
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