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# A doctor prescribed 18 cubic centimeters of a certain drug to a patien

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A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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28 Jun 2017, 02:06
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35% (medium)

Question Stats:

78% (01:22) correct 22% (02:12) wrong based on 42 sessions

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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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A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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28 Jun 2017, 03:36
Bunuel wrote:
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

Idea dosage for 120 pound weight = 120 * 2/15 = 16 cc
Dosage recommended earlier = 18 cc
Reduction = 2cc

Kindly note that 2cc need to be removed from 18 cc and not 16 cc
Reduction = 2/18 = 1/9

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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28 Jun 2017, 05:07
Bunuel wrote:
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

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)...
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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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28 Jun 2017, 06:45
Given data :
Doctor prescribes 18cc for 120pounds body weight (18:120 = 3:20)
Ideal dosage is 2cc : 15pounds.

3:20 is nothing but $$3*\frac{3}{4} : 20*\frac{3}{4}$$ = 2.25cc : 15 pounds

So the dosage(2.25cc) must be reduced by .25cc to bring it down to 2cc,

making percent change : $$\frac{.25cc}{2.25cc}= \frac{1}{9}$$ = 11.11%(Option C)
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A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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28 Jun 2017, 09:05
Bunuel wrote:
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

Quote:
If the typical dosage is 2 cubic centimeters per 15 pounds of body weight

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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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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29 Jun 2017, 01:56
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?

18 cubic centimeters =====> 120 pounds

Typical Dosage = 2 cubic centimeters =====> 15 pounds

120 Pounds Typical dosage $$= \frac{120}{15} * 2$$

$$= 8 * 2$$

$$= 16$$

Total dosage administered $$= 18$$

Additional dosage $$= 18 - 16$$ $$= 2$$

What % should be reduced? $$= \frac{2}{18} * 100 = 100/9 = 11.1$$

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien  [#permalink]

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30 Jun 2017, 09:22
Bunuel wrote:
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

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

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Re: A doctor prescribed 18 cubic centimeters of a certain drug to a patien   [#permalink] 30 Jun 2017, 09:22
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