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When a certain tree was first planted, it was 4ft tall, and [#permalink]
30 May 2008, 04:47

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When a certain tree was first planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for the next 6 yrs. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many ft. did the height of the tree increase each year? A) 3/10 B) 2/5 C) 1/2 D) 2/3 E) 6/5

OA is D, please show me how you solve this problem!

Initial tree height - 4 ft It grows at constant growth rate for next 6 years, say X ft/year At the end of 1 year, the tree height will be - 4 + X ft 2 year - 4 + 2X ft 3 year - 4 + 3X ft 4 year - 4 + 4X ft 5 year - 4 + 5X ft 6 year - 4 + 6X ft

At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year So, the difference in height between 6th year and 4th year is 1/5 the height of 4th year (4+4X ft) 6th year height - 4th year height = 1/5(4th year height) (4+6X) - (4+4X) = 1/5(4+4X) 2X = 1/5(4+4X) 10X = 4+4X 6X = 4 X = 2/3 So, growth per year - 2/3 ft