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, 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 feet did the height of the tree increase each year?
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tree problem
Source: Beat The GMAT — Problem Solving |
I Solved is slightly differently and got the foll equation
1/5(4+6x) = (4+4x) solving tis it comes to x = 8/7 or 1.14 feet every year
I am confused as to how you got 1.2 as the multiplication factor. clarification would be helpfull
Cheers.
1/5(4+6x) = (4+4x) solving tis it comes to x = 8/7 or 1.14 feet every year
I am confused as to how you got 1.2 as the multiplication factor. clarification would be helpfull
Cheers.
Height of the tree = 4raoulfernandes wrote:I Solved is slightly differently and got the foll equation
1/5(4+6x) = (4+4x) solving tis it comes to x = 8/7 or 1.14 feet every year
I am confused as to how you got 1.2 as the multiplication factor. clarification would be helpfull
Cheers.
Each year increases by X
1st year = x+4
2nd year=2x+4, so on an so forth
4th year=4x+4
6th year=6x+4
At the end of 6th year the tree was 1/5 taller than what it was in 4th
Therefore,
(6x+4) - (4x+4) = 1/5(4x+4)
(6x+4) = 1/5(4x+4) + (4x+4)
(6x+4) = (4x+4)(1+1/5)
(6x+4) = (4x+4)*6/5
(4x+4)6/5 = (6x+4)
24x+24 = 30x + 20
6x = 4
x = 2/3
I was making a comparison between year 4 and year 6, using 4 + 4x and 4 + 6x, respectively. I used 1.2 because the question explicitely states "At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year." 1/5 taller x times 1.2. hope that explains
parallel_chase wrote:raoulfernandes wrote:
At the end of 6th year the tree was 1/5 taller than what it was in 4th
Therefore,
(6x+4) - (4x+4) = 1/5(4x+4)
(6x+4) = 1/5(4x+4) + (4x+4)
(6x+4) = (4x+4)(1+1/5)
How did you get the (1+1/5)?
factor out (4x+4)pierce22884 wrote: How did you get the (1+1/5)?
fact that tree is 20 percent bigger in year 6 compared to year 4 indicates that it grew 20 percent. 20 percent in decimal is .2. A 20 percent increase on x is x times 1.2.
For those who do not want make any equations
* there is tab space between 4 , 2 and etc
Starting increse by 1 2 3 4 5 6
4 2 6 8 10 12 14 16 16-12 = 1/3 of 12
4 1 5 6 7 8 9 10 10-8=2 = 1/4 of 8
4 0.5 4.5 5 5.5 6 6.5 7 7-6=1= 1/6 of 6
so our answer should lie between 0.5 and 1
Thanks
Vishal Shah
* there is tab space between 4 , 2 and etc
Starting increse by 1 2 3 4 5 6
4 2 6 8 10 12 14 16 16-12 = 1/3 of 12
4 1 5 6 7 8 9 10 10-8=2 = 1/4 of 8
4 0.5 4.5 5 5.5 6 6.5 7 7-6=1= 1/6 of 6
so our answer should lie between 0.5 and 1
Thanks
Vishal Shah
