When a certain tree was planted

[guest612]

When a certain tree was 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

Answer: D. 2/3

Can you please tell me how to solve this problem? Also, can you help clarify if I'm calculating for 6 years or 7 years (because starting with Year 1 + 6 years)? I tried doing something along the lines of

year 4 =x
year 6 = x+(1/5)x

[tmmyc]

When the tree was planted, it was 4 feet tall. It then grows by a constant amount each year for 6 years. Call this constant amount 'x'.

Now: 4
1 year: 4+x
2 years: 4+2x
3 years: 4+3x
4 years: 4+4x
5 years: 4+5x
6 years: 4+6x

At the end of the 6th year, it was 1/5 taller than at the end of the 4th year. This means the 6th year height is 6/5 times the 4th year height (1 + 1/5 = 6/5).

(6/5)*(4+4x) = 4+6x

Solving for x, you get 2/3. The trees grows by 2/3 every year.

[RonPurewal]

When the tree was planted, it was 4 feet tall. It then grows by a constant amount each year for 6 years. Call this constant amount 'x'.

Now: 4
1 year: 4+x
2 years: 4+2x
3 years: 4+3x
4 years: 4+4x
5 years: 4+5x
6 years: 4+6x

At the end of the 6th year, it was 1/5 taller than at the end of the 4th year. This means the 6th year height is 6/5 times the 4th year height (1 + 1/5 = 6/5).

(6/5)*(4+4x) = 4+6x

Solving for x, you get 2/3. The trees grows by 2/3 every year.

splendid.

[guest612]

thank you both tymmc and ron. why do the questions seem harder? =(

[rfernandez]