Question
Find three consecutive positive even integers whose sum is 90.
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Answer
Let first positive even number = 2x
Second number = 2x + 2
Third number = 2x + 4
2x + 2x +2 + 2x + 4 = 90
⇒ 6x + 6 = 90
⇒ 6x = 90 - 6 = 84
x = 14
First even number = 2x = 2 × 14 = 28
Second number = 2x + 2 = 2 × 14 + 2 = 28 + 2 = 30
Third number = 30 + 2 = 32
Required numbers are 28, 30, 32
Second number = 2x + 2
Third number = 2x + 4
2x + 2x +2 + 2x + 4 = 90
⇒ 6x + 6 = 90
⇒ 6x = 90 - 6 = 84
x = 14
First even number = 2x = 2 × 14 = 28
Second number = 2x + 2 = 2 × 14 + 2 = 28 + 2 = 30
Third number = 30 + 2 = 32
Required numbers are 28, 30, 32
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