Problema Solution

find three consecutive odd positive integers such that 5 times the sum of all three is 66 more than the product of the first and second integers

Answer provided by our tutors

Every odd integer can be written as 2k + 1, where k is integer


The 3 consecutive odd positive integers can be written as:


2k - 1, 2k + 1, 2k + 3, where k is integer, 2k-1>0, k>1/2


5 times the sum of all three is 66 more than the product of the first and second integers:


5(2k - 1 + 2k + 1 + 2k + 3) = 66 + (2k - 1)(2k + 1)

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k = 5


2*5 - 1 = 9


2*5 + 1 = 11


2*5 + 3 = 13


The three consecutive odd positive integers are 9, 11 and 13.