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
⇒ 4x + 4 = 76
⇒ 4x = 76 – 4 = 72
x = 18
First number = 2x + 1 = 2 × 18 + 1 = 36 + 1 = 37
Second number = 2x + 3 = 2 × 18 + 3 = 36 + 3 = 39
Numbers are 37, 39
Second odd number = 2x + 3
2x + 1 + 2x + 3 = 76
⇒ 4x + 4 = 76
⇒ 4x = 76 – 4 = 72
x = 18
First number = 2x + 1 = 2 × 18 + 1 = 36 + 1 = 37
Second number = 2x + 3 = 2 × 18 + 3 = 36 + 3 = 39
Numbers are 37, 39
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