Find the consecutive positive odd integers whose sum is 76. - Vidyadip

Question

Find the consecutive positive odd integers whose sum is $76.$

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Answer

Let first odd number $= 2x + 1$
Second odd number $= 2x + 3 $
$2x + 1 + 2x + 3 = 76$
$ \Rightarrow 4x + 4 = 76 $
$\Rightarrow 4x = 76 – 4 = 72 $
$x = 18$
First number $= 2x + 1 $
$= 2 \times 18 + 1 $
$= 36 + 1 $
$= 37$
Second number $= 2x + 3 $
$= 2 \times 18 + 3 $
$= 36 + 3 = 39$
Numbers are $37, 39$

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