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

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

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Answer 1 · 2016-07-06T05:33:04

${193, 194, 195}$ ${193, 194, 195}$

Explanation:

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

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

$\Rightarrow 3 n + 3 = 582$ $=> 3n+3 = 582$

$\Rightarrow 3 n = 582 - 3 = 579$ $=> 3n = 582-3 = 579$

$\Rightarrow n = \frac{579}{3} = 193$ $=> n = 579/3 = 193$

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

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

Answer 2 · 2016-07-06T05:40:38

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

Explanation:

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

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

Observe that they fulfil the given cond.

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

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

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