I believe that the answer choices have been transcribed incorrectly.
When this problem was posted in 2015, the answer choices read as follows:
A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?
(A) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%
Goal: To decrease the number of peanuts as much as possible.
Constraint: The remaining peanuts must constitute more than 1/2 of the remaining nuts.
We can PLUG IN THE ANSWERS, which represent the greatest percentage by which the number of peanuts can be decreased.
Since the total number of nuts cannot be greater than 75 -- and P : C : A = 10:4:1 = 50:20:5 -- let P=50, C=20, and A=5, for a total of 75 nuts.
Since the question stem asks for the greatest possible percentage, start with the greatest answer choice.
Answer choice E:
If the number of peanuts is reduced by 58%, we get:
New P = 50 - (58/100)(50) = 50 - 29 = 21.
New total = New P + C + A = 21+20+5 = 46.
New P/New total = 21/46, which is less than 1/2.
Since the new number of peanuts is not more than 1/2 of the new total, eliminate E.
Answer choice D:
If the number of peanuts is reduced by 50%, we get:
New P = 50 - (50/100)(50) = 50 - 25 = 25.
New total = New P + C + A = 25+20+5 = 50.
New P/New total = 25/50, which is equal to 1/2.
Since the new number of peanuts is not more than 1/2 of the new total, eliminate D.
Answer choice C.
If the number of peanuts is reduced by 49%, we get:
New P = 50 - (49/100)(50) = 50 - 49/2 = 25.5.
Since the new number of peanuts must be an integer, eliminate C.
Answer choice B:
If the number of peanuts is reduced by 48%, we get:
New P = 50 - (48/100)(50) = 50 - 24 = 26.
New total = New P + C + A = 26+20+5 = 51.
New P/New total = 26/51, which is greater than 1/2.
Success!
The correct answer is
B.
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