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Doesn't seem hard, but for some reason I'm drawing a blank!

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Joined: 12 Oct 2006
Posts: 81
Location: NJ, US
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Doesn't seem hard, but for some reason I'm drawing a blank! [#permalink]  23 Oct 2006, 12:37
Doesn't seem hard, but for some reason I'm drawing a blank! Here's how it breaks down:

- tree 4 ft tall when planted
- height increased by a constant amount each year for 6 years
- end of the 6th year the tree was 1/5 taller than it was at end of the 4th year.
- by how many ft. did the height of the tree increase each year???

I know this is something simple that I am not seeing so any help would be great. Thanks!
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Joined: 01 May 2006
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Let define some variables

- tree 4 ft tall when planted
a(0) = 4

- height increased by a constant amount each year for 6 years
a(n) = a(0) + n * x with x = the constant increase and n <= 6 years

- end of the 6th year the tree was 1/5 taller than it was at end of the 4th year.
a(6) = a(4) *(1+1/5)

- by how many ft. did the height of the tree increase each year???

Since, a(4) = 4 + 4*x = 4*(1+X)

Thus, 4*(1+X)*(1+1/5) = 4 + 6*x
<=> 24/5*(1+x) = 4 + 6*x
<=> 24 + 24*x = 20 + 30*x
<=> x = 4/6 = 2/3
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