datonman wrote:At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
An alternate approach is to PLUG IN THE ANSWERS, which represent the number of oranges that must be put back.
Before any oranges are put back, the total cost of the 10 pieces of fruit = 10*56 = 560.
When the correct answer choice is plugged in, the average cost will decrease to 52 cents.
Answer choice D: 4 oranges put back
Resulting total cost after 4 60-cent oranges are put back = 560 - (4*60) = 320.
Average price of the remaining 6 pieces of fruit = 320/6 = 53+.
The average price is too high.
Eliminate D.
Since oranges are more expensive than apples, the average price will decrease to 52 cents only if MORE oranges are put back.
The correct answer is
E.
Answer choice E: 5 oranges put back
Resulting total cost after 5 60-cent oranges are put back = 560 - (5*60) = 260.
Average price of the remaining 5 pieces of fruit = 260/5 = 52.
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