The sum of three consecutive integers equal 417. What are the integers?

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Answer 1 · 2016-08-19T12:08:38

The integers are $138; 139 and 140$ $138;139 and 140$

Let the three consecutive integers be $(a - 1); a; and (a + 1)$ $(a-1); a; and (a+1)$

So we can write sum of these as

$(a - 1) + a + (a + 1) = 417$ $(a-1)+a+(a+1)=417$

or

$3 a = 417$ $3a=417$

or

$a = \frac{417}{3}$ $a=417/3$

or

$a = 139$ $a=139$

therefore the integers are $138; 139 and 140$ $138;139 and 140$

Answer 2 · 2016-08-19T12:09:12

$138, 139, 140$ $138,139,140$

Call the middle number $x$ $x$ so the three consecutive integers will be $(x - 1), x, (x + 1)$ $(x-1),x,(x+1)$

Summing:

$(x - 1) + x + (x + 1) = 417$ $(x-1) + x + (x+1) = 417$

$3 x = 417$ $3x = 417$

$x = 139$ $x = 139$

Middle number is 139 so numbers are 138, 139, 140