A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of body weight, by what percent should the prescribed dosage be reduced to bring it down to the typical dosage?

(A) 7.5
(B) 9.0
(C) 11.1
(D) 12.5
(E) 14.8
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Typical dosage is \(2\) cubic centimeters per \(15\) pounds \(= \frac{2}{15}\)

Let the typical dosage be \(x\) cubic centimeters for \(120\) pounds \(= \frac{x}{120}\)

\(\frac{2}{15} =\frac{x}{120}\)

\(x = \frac{2*120}{15} = 16\)

Therefore typical dosage for \(120\) pounds is \(16\) cubic centimeters.

Doctor prescribed \(18\) cubic centimeters for \(120\) pounds.

Difference \(= 18 - 16 = 2\)

We need to find the difference ie; \(2\) is what percentage of the dosage doctor has prescribed \(18\).

Required percent \(= \frac{2}{18} * 100 = 11.1\) . Answer (C)...

So, 1 pound requires \(\frac{2}{15}\) cc
Or, 120 pound requires \(\frac{2}{15}*180\) cc = \(16\) cc

The doc gave 18 cc, and the patient needs 16 cc

Thus, the doc must reduce dosage by 2 cc

So, the percentage reduction required is \(\frac{2}{18} *100= 11.11\) %

Hence, the correct answer must be (C) 11.11 %
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We are given that the typical rate is (2 cm^3)/(15 lbs). Thus a patient whose weight was 120 lbs should be prescribed 120 lbs x (2 cm^3)/(15 lbs) = 240/15 = 16 cm^3 of the drug.

However, since a doctor prescribed 18 cm^3 of the drug, we can let n = the percentage decrease needed and create the following equation:

18(1 - n/100) = 16

1 - n/100 = 16/18

2/18 = n/100

18n = 200

n = 11.11

Answer: C
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