A certain kudzu plant was 11 feet long on the day it was

Question

A certain kudzu plant was 11 feet long on the day it was planted, and the length grows by a constant amount every day (including the first day it was planted). If this plant grew 40% between the fourth day after it was planted and the tenth day after it was planted, how many feet per day does it grow?

OA:  1 foot per day

I copied a problem from ΜGMAT book that I find difficult to translate into math and would appreciate if someone had the time to walk me through. I don't want the solution to this problem. I just want someone to explain how I translate the colored sentence.

I understand its an arithmetic progression - linear growth because it says by a constant amount every day.

11 ,t=0 should I think of it as the start of the first day?
11+x , t=1 should I think of it as the start of the second day or the end of the first day?
11+2x ,t=2 .....

Should t=0 be 11+x because it said that it grew the first day that was planted?

would it be easier if I named the day it was planted as t=1?

what will the fourth day after it was planted be? t=4 or t=5?

Any thoughts?

Bunuel · Accepted Answer

A certain kudzu plant was 11 feet long on the day it was planted, and the length grows by a constant amount every day (including the first day it was planted). If this plant grew 40% between the fourth day after it was planted and the tenth day after it was planted, how many feet per day does it grow?

The length of the plant after the fourth day is  11+4x , where x is the growth rate per day.
The length of the plant after the tenth day is  11+10x .

We are given  11+10x=1.4(11+4x)  --> x=1 foot per day.

Hope it's clear.

u0422811 · Answer

Day of planting would be day 0. So fourth day after would be T=4.

You are correct on your formula of 11 + X(days) = Ending Height

Hope that helps. Let me know if you need more.

rvinodhini · Answer

Hi

Need help in solving the problem

A certain plant was 11 feet long on the day it was planted & the length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 40% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow

a) 2
b) 4.5
c) 1
d) 5.5
e) 3

Thanks

GyanOne · Answer

If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).

Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.

Therefore 6k = 0.4 (11 + 4k) 
=> k = 1

Therefore the plant grows by 1 feet every day.

Option (C)

penguinman · Answer

I am having trouble with the wording of this problem, can someone please explain "the fourth day after it was planted"

When I worked it out I got An = (n+1)x+11 vs the solution is An = nx+11. I added an extra day because I thought it was the fourth day after the planting, and the problem also says it grows by the constant rate on the first day it was planted so A0 = 11+x, A1 = 11+2x, etc...thanks!

SVaidyaraman · Answer

1. The height on the fourth and tenth days are related with one unknown which is the growth amount. Solved by equating the two expressions 
2. The plant grows by a constant amount every day. Let that be x. 
3. After 4 days it would have grown by 4x
4. After 10 days it would have grown by 10x.
5. Initial height is 11 feet.
6. Height after 4 days is 11+ 4x
7. Height after 10 days is 11 + 10x
8. (6) and (7) can be related by multiplying the factor 1.4 with (6) 
9. 1.4*(11+4x) = 11+10x
10 x is 1 or the the plant grows 1 foot per day

rrsnathan · Answer

Hi Bunuel,

I have a doubt
In this problem 40% growth is between 4th day and 10th day right? so how come we can multiply the 1.4(for 40 %) to 11+4x, where 11+4X is for 4th day, not the days between the 4ht and 10th.

We should multiply 1.4 to the days between 4th and 10th right?
Please help me in this

ConnectTheDots · Answer

We are not comparing growth. We are comparing height.

Initial Height = 11
Constant growth everyday = x

After 4 days, height(H4) = 11 + 4x
After 10 days, height(H10) = 11 + 10x

40% growth between H4 and H10, means:
0.4 = (H10 - H4)/H4
=> 0.4*H4 = H10 - H4
=> 0.4H4 + H4 = H10
=> 1.4*H4 = H10

Substitute values, 
1.4*(11+4x) = (11 + 10x)
=> x = 1 (skipped the solving part)

Alternatively,

After 4 days, height(H4) = 11 + 4x
After 10 days, height(H10) = 11 + 10x
Growth = H10 - H4 = (11+10x) - (11+4x) = 6x

% Growth: 6x/(11+4x) = 0.4
=> 6x = 0.4*(11+4x)
=>60x = 4 *(11+4x) = 44 + 16x
=> 44x = 44
=> x = 1

bumpbot · Answer

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A certain kudzu plant was 11 feet long on the day it was

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A certain kudzu plant was 11 feet long on the day it was

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