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Question

find 3 consecutive natural number whose sum is 11

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Solution

No three consecutive natural numbers when added will give you a sum of 11. So the question is wrong.
I will answer two similar questions in my referance book. I hope one of them is the question you meant to ask. If not, you can understand the technique from these and apply it to complete your answer.

1.What are three consecutive number whose sum is 111?
Ans.

One number is n, the consecutive is n+1 and the following one is n+2. Then you are asking

n+(n+1)+(n+2)=111

3n+3=111

3n=108

n=1083=36

so the first number is 36, the second is 37 and the third is 38.

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2. find three consecutive integers whose sum is 11 more than twice the greatest of the three integers.
Ans.

let the three numbers be x, x+1 and x+2
x + x+1 x+2 = 11 + 2(x+2)
Combine like terms and distribute the 2 on the right
3x + 3 = 11 + 2x + 4
3x - 2x + 3 - 3 = 11 + 2x - 2x + 4 - 3
x = 11 + 4 - 3
x = 12
Integers are 12, 13 and 14

Proof
12 + 13 + 14 = 39
11 + 2(12+2) = 11 + 2(14) = 11 + 28 = 39

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Hope I have cleared your doubts..

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