OG 108
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Algebraic Approach:[email protected] wrote:Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period?
A. 1250
B. 1563
C. 2250
D. 2560
E. 2752
The number of trees in a year is increased by 1/4 of the number of trees in the preceding year. Hence, number of trees in a year = (1 + 1/4) = 5/4 of the number of trees in the preceding year.
Let us assume that number of trees at the beginning of the year = N
So, N*(5/4)*(5/4)*(5/4)*(5/4) = 6250
--> N = 6250*(4/5)*(4/5)*(4/5)*(4/5) = 6250*(4^4)/(5^4) = 6250*256/625 = 2560
The correct answer is D.
