Question

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

Answer 1

`44,45,46`

Explanation:

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

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

`"and the third integer " n+2`

`rArrn+n+1+n+2=135larrcolor(blue)" sum of integers"`

`rArr3n+3=135larrcolor(blue)" simplifying left side"`

`"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"`