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Simple problem?

by H2O » Wed Jul 16, 2008 8:52 am
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amont 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 correct
(e) 6/5

My first answer was that the tree grew 1/10 each year since between year 4 and 6 it grew 1/5. But that's not one of the choices and it's too easy to be a solution anyway.
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by anksanks » Wed Jul 16, 2008 9:05 am
let the increase in height each year be x
initial height = 4
after 1 year= 4+x
after 2 years = 4+2x
after 3 years = 4+3x
after 4 years = 4+4x
after 5 years = 4+5x
after 6 years = 4+6x

Given --> height at 6 years is 1/5 more then that at 4 years
=> 4+6x =(1 + 1/5) * ( 4 +4x)
=> 4 + 6x = (6/5) * (4 + 4x)
=> 20 + 30x = 24 + 24x
=> 6x = 4
=> x = 2/3
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Wrap me all around,
Define this adorable thought,
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by AleksandrM » Wed Jul 16, 2008 9:14 am
Not that it makes a big difference but you could also set it up the other way around:

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

10x = 4 + 4x

x = 2/3
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by moliver » Wed Jul 16, 2008 6:40 pm
as anksanks says,at year 4 the height must be:
year 4 = 4+4x
and for the 6 year:
year 6 = 4+6x

then you now that the relation between the 4 year and the 6 year is:
year 6 = year 4 + (year 4)/5
so
4+6x = 4+4x + (4+4x)/5
4+6x = 4+4x + 4/5 + 4x/5
6x/5 = 4/5
=> x= 2/3
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by Mclaughlin » Wed Jul 16, 2008 7:41 pm
I'm not clear why you can divide 4+4x by 5.

Please explain why you can do that. I would've not done that and been messed up. I know it's grown by 1/5ft but not sure why all that over 5.
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by H2O » Wed Jul 16, 2008 7:51 pm
Could you please explain how you got (1+1/5)(4+4x) part of the equation. I get the first part.

and

why do we have 4+4x/5 in the other example?

Thank you!
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by moliver » Thu Jul 17, 2008 3:38 am
At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year.
So at the 6 year the height is: year 6 = 4+6x
and the 6year is also 1/5 taller than it was at the end of the 4 year.
So we need what height was at the end of the 4 year.
And that height plus 1/5 is going to be the height of the year 6.
year 4 = 4 + 4x
year 6= year 4 + (year 4)/5

better?
please tell me if not.
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