gmatblood wrote:when a certain tree was first planted, it was 4 feet tall and the geight of the tree increased by a constant and each year for the next 6 years. At the end of the 6th year, tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of three increse every year?
A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. Since we know that the growth is by a constant amount, we have a linear growth problem. Thus, we can let x = the yearly growth amount in feet:
Starting height = 4
Height after year one = 4 + x
Height after year two = 4 + 2x
Height after year three = 4 + 3x
Height after year four = 4 + 4x
Height after year five = 4 + 5x
Height after year six = 4 + 6x
We are also given that at the end of the 6th year the tree was 1/5 taller than it was at the end of the 4th year. This means the height of the tree at the end of the 6th year is 6/5 times as tall as its height at the end of the 4th year. Thus, we can create the following equation:
(6/5)(4 + 4x) = 4 + 6x
To eliminate the fraction 6/5, we multiply the entire equation by 5:
6(4 + 4x) = 20 + 30x
24 + 24x = 20 + 30x
6x = 4
x = 4/6 = 2/3 feet
Answer:
D
