chieftang wrote:How many grams of a 1% hydrocoritzone ointment and how many grams of a 2.5% hydrocortizone ointment must be mixed to create 120 grams of a 2% hydrocortizone ointment?
(A) 110g 1% hydrocortizone, 10g 2.5% hydrocortizone
(B) 100g 1% hydrocortizone, 20g 2.5% hydrocortizone
(C) 90g 1% hydrocortizone, 30g 2.5% hydrocortizone
(D) 80g 1% hydrocortizone, 40g 2.5% hydrocortizone
(E) 70g 1% hydrocortizone, 50g 2.5% hydrocortizone
Since the percentage of hydrocortizone in the mixture (2%) is closer to 2.5% than to 1%, more than half of the mixture -- more than 60 grams -- must come from the 2.5% ointment.
Thus, none of the answer choices is correct.
What is the source of this question?
To determine the required ratio of 1% ointment to 2.5% ointment, we can use
alligation, which dictates the following:
The proportion needed of each ingredient in the mixture is equal to the distance between the OTHER TWO PERCENTAGES.
Proportion needed of the 1% ointment = |percentage in the mixture - percentage in the other ointment| = |2 - 2.5| = .5
Proportion needed of the 2.5% ointment = |percentage in the mixture - percentage in the other ointment| = |2 - 1| = 1.
Ratio of 1% ointment to 2.5% ointment = .5:1 = 1:2.
Since the mixture is 120 grams, and 1:2 = 40:80, the mixture must contain 40 grams of the 1% ointment and 80 grams of the 2.5% ointment.
If the answer choices contained the correct answer, an alternate approach would be plug in the answer choices.
Since .02(120) = 2.4, the correct answer choice would need to yield 2.4 grams of hydrocortizone.
Answer choice: 40 grams 1% ointment, 80 grams 2.5% ointment
Amount of hydrocortizone in the 1% ointment = .01(40) = .4 grams.
Amount of hydrocortizone in the 2.5% ointment = (.025)80 = 2 grams.
Total amount of hydrocortisone = .4 + 2 = 2.4 grams. Success!
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