If the first and third of three consecutive odd integers are added, the result is 57 less than five times the second integer. How do you find the third integer?

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Answer 1 · 2017-05-09T11:31:14

The third integer is $21$

Let the three consecutive odd integers be $2n-1 , 2n+1 and 2n+3$

By condition , $(2n-1) +(2n+3) = 5(2n+1) -57$ or

$2n-1 +2n+3 = 10n + 5 -57 or 4n +2 =10n -52 or 6n =54 or n =9$

Three consecutive odd integers are $2n-1= 17 , 2n+1= 19 and 2n+3 =21$

The third integer is $21$ [Ans]