The sum of three consecutive integers is 135. What are the numbers?

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The sum of three consecutive integers is 135. What are the numbers?

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Answer 1 · 2017-07-04T07:57:49

$44, 45, 46$ $44,45,46$

Explanation:

$let the first integer be represented by n$ $"let the first integer be represented by " n$

$then the second integer will be n + 1$ $"then the second integer will be " n+1$

$and the third integer n + 2$ $"and the third integer " n+2$

$\Rightarrow n + n + 1 + n + 2 = 135 \leftarrow sum of integers$ $rArrn+n+1+n+2=135larrcolor(blue)" sum of integers"$

$\Rightarrow 3 n + 3 = 135 \leftarrow simplifying left side$ $rArr3n+3=135larrcolor(blue)" simplifying left side"$

$subtract 3 from both sides$ $"subtract 3 from both sides"$

$3ncancel(+3)cancel(-3)=135-3$

$rArr3n=132$

$"divide both sides by 3"$

$(cancel(3) n)/cancel(3)=132/3$

$rArrn=44$

$rArrn+1=44+1=45$

$rArrn+2=44+2=46$

$"the three consecutive integers are " 44,45,46$

$color(blue)"As a check"$

$44+45+46=135rarr" True"$

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The sum of three consecutive integers is 135. What are the numbers?

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