Problem Solving

When a certain tree is planted, it was 4 ft 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?

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5

Height of tree day 0 = 4
Let d be the increased height each year
Height of tree at the end of the 1st year = 4+d
Height of tree at the end of the 2nd year = 4+d+d = 4+2d
Height of tree at the end of the 3rd year = 4+d+d+d = 4+3d
Height of tree at the end of the 4th year = 4+d+d+d+d = 4+4d
Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4+5d
Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4+6d

We are told that 4+6d is 1/5 greater than 4+4d
In other words 4+6d = (4+4d) + 1/5(4+4d)
or 4+6d = 6/5(4+4d)
Multiply both sides by 5 and (to eliminate fractions) and solve for d to get d = [spoiler]2/3[/spoiler]

The answer is D

Cheers,
Brent

ela07mjt wrote:Hi Brent

Whilst doing the question, I got stuck at this question on below step...I still can't fully grasp the concept. Please could you explain in more detail or suggest an alternative approach?


We are told that 4+6d is 1/5 greater than 4+4d
In other words 4+6d = (4+4d) + 1/5(4+4d)

Sure thing.
Let's look at a few examples.

Let's let J = John's age
If Al's age is 1/5 greater than John's age, then to find Al's age, we take John's age (J) and add 1/5 of J to get: J + (1/5)J (this represents Al's age)

Aside: another way to look at it is to say that Al's age is 20% greater than John's age (since 20% greater is the same as 1/5 greater)

So, if 4+6d is 1/5 greater than 4+4d, then we can conclude that 4+6d = (4+4d) + 1/5(4+4d)

I hope that helps.

Cheers,
Brent