The sum of three consecutive integers is 582. What are the integers?

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Answer 1 · 2016-07-06T05:33:04

#{193, 194, 195}#

Let #n# be the least of the integers. Then the next two consecutive integers are #n+1# and #n+2#, and we have

#n+(n+1)+(n+2) = 582#

#=> 3n+3 = 582#

#=> 3n = 582-3 = 579#

#=> n = 579/3 = 193#

Therefore the three consecutive integers are #{193, 194, 195}#

Checking our answer, we find that #193+194+195 = 582#, as desired.

Answer 2 · 2016-07-06T05:40:38

The reqd. ints. are, #193,194, & 195.#

We require consecutive integers, so, if we start with #x#, the following/succeeding ints. must be #x+1# & #(x+1)+1=x+2#.

Then, by what is given, #x+(x+1)+(x+2)=582#, i.e., #3x+3=582#, or, #3x=582-3,=579#, giving, #x=579/3,=193; (x+1)=194, &, (x+2)=195.#

Observe that they fulfil the given cond.

The reqd. ints. are, #193,194, & 195.#