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 $37, 39.$
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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