Q. 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 the body weight, by what percent was the
prescribed dosage greater than the typical dosage?
A) 8% B) 9% C) 11% D) 12.5%
E) 14.8%
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We can use equivalent ratios to determine what the dosage SHOULD have been.Joy Shaha wrote:Q. 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 the body weight, by what percent was the
prescribed dosage greater than the typical dosage?
A) 8%
B) 9%
C) 11%
D) 12.5%
E) 14.8%
We'll use the ratio of drug dosage (in cubic centimeters)/body weight (in pounds)
Let x = the dosage (in cubic centimeters) the patient SHOULD have received
We get: 2/15 = x/120
Cross multiply to get: 15x = (2)(120)
Simplify: 15x = 240
Solve: x = 16
So, the patient SHOULD have received a dosage of 16 cubic centimeters
Instead, the patient was prescribed a dosage of 18 cubic centimeters
Percent increase = 100(new - original)/original
= 100(18 - 16)/16
= 200/16
= 12.5
Answer: D
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Slightly different approach:
First divide the body weight by 15 to understand how many of the 2 cubic centimentres dose.
120/15 = 8
Thus, he should have been prescribed 8 x 2 cubic centimetre dosages = 16 cubic centimetre dosage.
However, the prescription is for 18 cubic cm, which is 2 cubic cm more than the adequate dosage of 16 cubic cm. This excess should be calculated on the base of 16 cubic cm.
Thus, we need to know the percentage for 2/16 = 1/8. It is ideal to know the percentages of a few fractions on your fingertips to know that 1/8 translates to 12.5% directly.
Thus, the answer is D 12.5%
First divide the body weight by 15 to understand how many of the 2 cubic centimentres dose.
120/15 = 8
Thus, he should have been prescribed 8 x 2 cubic centimetre dosages = 16 cubic centimetre dosage.
However, the prescription is for 18 cubic cm, which is 2 cubic cm more than the adequate dosage of 16 cubic cm. This excess should be calculated on the base of 16 cubic cm.
Thus, we need to know the percentage for 2/16 = 1/8. It is ideal to know the percentages of a few fractions on your fingertips to know that 1/8 translates to 12.5% directly.
Thus, the answer is D 12.5%
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