Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.

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Solution

Let the first number be x.

According to the question second number is x + 1 and the third is x + 2

Sum of first and second numbers = (x) + (x + 1).

According to question:

$\Rightarrow (x) + (x + 1) = 15 + (x + 2)$

$\Rightarrow 2 x + 1 = 17 + x$

Transposing x to LHS and 1 to RHS, we get

$\Rightarrow 2 x - x = 17 - 1$

$\Rightarrow x = 16$

So, first number = x = 16,

Second number = x + 1 = 16 + 1 = 17

And third number = x + 2 = 16 + 2 = 18

Thus, the required consecutive natural numbers are 16, 17 and 18.

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