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

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07 Nov 2008, 09:12

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

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

There's something particular with the answer of this one which i don't understand, hence the posting.

height at the end of 6th yr = 4 + x + x + x + x + x + x = 4 + 6x height at the end of 4th yr = 4 + x + x + x + x = 4 + 4x

We have to read the question carefully to make sure we see that the end of the 6th year is being compared to the end of the 4th year. Also note that the tree grows by a constant amount each year. This is different than the same % each year.

Let x = the constant annual growth in feet.

4ft is the original height of the tree, so after the 6th year, we have

4 + x + x + x + x + x + x….aslo 4 + 6x

After the 4th year we have 4 + x + x + x+ x or 4 + 4x

Lets compare the two values algebraically as the problem does:

6th year is 1/5 taller than the 4th year.

The difference in growth from the 4th to the 6th year will be 1/5 (or 0.2) of the height after the 4th year.

So…(4+6x)-(4+4x) = 1/5(4+4x)…now solve for x

4 + 6x -4 – 4x = 4/5 + 4/5x 2x = 4/5 + 4/5x Subtract 4/5x from both sides. I’ve changed 2x into 10/5x to easily do the subtraction of fractions.

10/5x – 4/5x = 4/5

6/5x = 4/5

Divide both sides by 6/5, which is the same as multiplying by 5/6

X = 4/5 * 5/6. (Reduce the 5’s or multiply out and) you have 20 / 30 or x = 2/3.

Hope a different approach may help someone else.

gameCode wrote:

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

There's something particular with the answer of this one which i don't understand, hence the posting.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Thanks Jallen. Its a bit clear now. I was wondering how 1/5 taller led to 1+1/5 . The wordings are very difficult for this one. I would have thought its either 1/5th or addition of 1/5. I knew the height after 6 years could not be 1/5th of height after 4 years. So i thought it might be addition. But i could not really understand why its so peculiar with this qs, i have not seen any other qs of this type. Is there any other similar example anyone has seen so far ?

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

There's something particular with the answer of this one which i don't understand, hence the posting.

Let the rate of increase be \(x\) feet per year.

At the end of the 4th year the height was \(4+4x\) and at the of the 6th year the height was \(4+6x\), which was "1/5 taller than it was at the end of the 4th year" --> \((4+4x)+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Lets concise equation a bit more. if x is the constant growth then difference between end of 6th year and end of 4th year is 2x. So 2x=(4+4x)/5 10x=4+4x 6x=4 x=2/3

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

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10 Jun 2013, 08:06

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gameCode wrote:

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

According to my method, I got a totally different answer. I am comfortable with all the explanations to this question but please help me finding flaw in my solution, here it is:

I considered it as a A.P. whose first term is 4.

I supposed 4th term to be 5x. Hence 6th term will me (5x+5x/5)=6x

as per A.P. formula [n-th term = a+(n-1)d]

4th term = 5x = 4+3d 6th term = 6x = 4+5d

After solving these equation for "d", I got d=4/7. What am I doing wrong ???
_________________

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

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10 Jun 2013, 22:40

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stunn3r wrote:

gameCode wrote:

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

According to my method, I got a totally different answer. I am comfortable with all the explanations to this question but please help me finding flaw in my solution, here it is:

I considered it as a A.P. whose first term is 4.

I supposed 4th term to be 5x. Hence 6th term will me (5x+5x/5)=6x

as per A.P. formula [n-th term = a+(n-1)d]

4th term = 5x = 4+3d 6th term = 6x = 4+5d

After solving these equation for "d", I got d=4/7. What am I doing wrong ???

Here is something wrong

the 1st term is 4 and after a year it will be 4+d and so on after the 4th year it will be 4+4d

5th term will be = 5x = 4+4d and 7th term will be 6x = 4+6d

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

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10 Jun 2013, 22:43

ichauhan.gaurav wrote:

stunn3r wrote:

gameCode wrote:

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

According to my method, I got a totally different answer. I am comfortable with all the explanations to this question but please help me finding flaw in my solution, here it is:

I considered it as a A.P. whose first term is 4.

I supposed 4th term to be 5x. Hence 6th term will me (5x+5x/5)=6x

as per A.P. formula [n-th term = a+(n-1)d]

4th term = 5x = 4+3d 6th term = 6x = 4+5d

After solving these equation for "d", I got d=4/7. What am I doing wrong ???

Here is something wrong

the 1st term is 4 and after a year it will be 4+d and so on after the 4th year it will be 4+4d

5th term will be = 5x = 4+4d and 7th term will be 6x = 4+6d

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

There's something particular with the answer of this one which i don't understand, hence the posting.

Let the rate of increase be \(x\) feet per year.

At the end of the 4th year the height was \(4+4x\) and at the of the 6th year the height was \(4+6x\), which was "1/5 taller than it was at the end of the 4th year" --> \((4+4x)+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.

Hi Bunuel,

Could you please help me with a fundamental issue?

For such problems, I am not sure whether the increase is by a factor(multiplication) or by an amount(addition). In this problem, I actually took it as multiplication and got the below equation

4a^6=4a^4(1+1/5) .. where a is the amount it increases by every year.

How do I differentiate between a multiplication increase and an addition increase?

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

There's something particular with the answer of this one which i don't understand, hence the posting.

Let the rate of increase be \(x\) feet per year.

At the end of the 4th year the height was \(4+4x\) and at the of the 6th year the height was \(4+6x\), which was "1/5 taller than it was at the end of the 4th year" --> \((4+4x)+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.

Hi Bunuel,

Could you please help me with a fundamental issue?

For such problems, I am not sure whether the increase is by a factor(multiplication) or by an amount(addition). In this problem, I actually took it as multiplication and got the below equation

4a^6=4a^4(1+1/5) .. where a is the amount it increases by every year.

How do I differentiate between a multiplication increase and an addition increase?

Thanks.

We are told that "the height of the tree increased by a constant amount each year" so it must be addition. If it were multiplication then the increase wouldn't be the same each year.

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

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14 Jul 2013, 02:54

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

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

Merging similar topics. Please refer to the solutions above.
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