How do you find three consecutive odd integers whose sum is 13 more than twice the largest of the three?

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Answer 1 · 2016-01-24T01:02:48

Interpret the description in terms of an unknown smallest integer #n# and solve to find integers:

#15, 17, 19#

Suppose the three odd integers are #n#, #n+2# and #n+4#

Their sum is:

#n + (n+2) + (n+4) = 3n+6#

#13# more than twice the largest of the three is:

#2(n+4)+13 = 2n+21#

From what we are told these two are equal:

#3n+6 = 2n+21#

Subtract #2n+6# from both sides to get:

#n = 15#

So the three integers are:

#15, 17, 19#