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When a certain tree was first planted, it was 4 feet tall,

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When a certain tree was first planted, it was 4 feet tall, [#permalink]

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25 Dec 2007, 07:35
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When a certain tree was first planted, it was 4 feet tall, and the height of the tree invreased 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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Re: PS - Tree height [#permalink]

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25 Dec 2007, 07:45
gregspirited wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree invreased 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

simplest method:

planted length: X=4
annual increase: Y

X,(X+Y),(X+2Y),(X+3Y),(X+4Y),(X+5Y),(X+6Y)

X+4Y+(X+4Y)/5=X+6Y
X+4Y=10
4+4Y=10
Y=3/2

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Re: PS - Tree height [#permalink]

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25 Dec 2007, 14:26
Ravshonbek wrote:
gregspirited wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree invreased 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

simplest method:

planted length: X=4
annual increase: Y

X,(X+Y),(X+2Y),(X+3Y),(X+4Y),(X+5Y),(X+6Y)

X+4Y+(X+4Y)/5=X+6Y
X+4Y=10
4+4Y=10
Y=3/2

Yes this is the simplest approach. however final answer should be 2/3 but not 3/2.

X+4Y+(X+4Y)/5=X+6Y

X+4Y=10Y ==> X=6Y==>Y=X/6=4/6=2/3.

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Re: PS - Tree height [#permalink]

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07 Jan 2008, 11:59

X+4Y+(X+4Y)/5=X+6Y UNDERSTOOD
X+4Y=10 WHERE IS THIS 10 COMING FROM?....
4+4Y=10 WHAT HAPPEN WITH THE X?
Y=3/2

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Re: PS - Tree height [#permalink]

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07 Jan 2008, 12:15
gregspirited wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree invreased 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

4+6x=6/5(4+4x) --> 24/5+24x/5=4+6x --> 24/5-4=6x-24x/5 --> 24/5-20/5=30x/5-24x/5

4/5=6x/5 --> 20=30x --> x=2/3

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Re: PS - Tree height [#permalink]

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07 Jan 2008, 12:24
gregspirited wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree invreased 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

4+5x=(4+3x)*1.2
4+5x=4.8+3.6x
1.4x=0.8
x=4/7

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Re: PS - Tree height [#permalink]

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07 Jan 2008, 12:38
correct reasoning, but note: it says at the end of the 6th and 4th years
i.e. 4+6x = (4+4x)*1.2

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Re: PS - Tree height [#permalink]

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07 Jan 2008, 14:22

Let h be the constant increase in height each year.

So heights at end of each year => 4 + h, 4 + 2h, 4 + 3h, 4 + 4h, 4 + 5h, 4 + 6h

At end of 6 year, the tree is 1/5th taller than at the end of the 4th year, i.e.

( 4 + 6h ) – ( 4 + 4h ) = 1/5 * ( 4 + 4h)

=> 2h = 1/5 * ( 4 + 4h )
=> h = 2 / 3

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Re: PS - Tree height   [#permalink] 07 Jan 2008, 14:22
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