If the average of 5 consecutive integers is 12, what is the sum of the least and greatest of the 5 integers?

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If the average of 5 consecutive integers is 12, what is the sum of the least and greatest of the 5 integers?

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Answer 1 · 2017-05-26T10:37:53

$24$ $24$

Explanation:

$let the 5 consecutive integers be$ $"let the 5 consecutive integers be"$

$n, x n + 1, x n + 2, x n + 3, x n + 4$ $n,color(white)(x)n+1,color(white)(x)n+2,color(white)(x)n+3,color(white)(x)n+4$

$\Rightarrow sum of the 5 integers = 12 \times 5 = 60$ $rArr"sum of the 5 integers" =12xx5=60$

$= n + (n + 1) + (n + 2) + (n + 3) + (n + 4) = 5 n + 10$ $=n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10$

$\Rightarrow 5 n + 10 = 60 \leftarrow and solving for n$ $rArr5n+10=60larr" and solving for n"$

$\Rightarrow n = 10$ $rArrn=10$

$\Rightarrow 10, x 11, x 12, x 13, x 14 \leftarrow are the 5 integers$ $rArr10,color(white)(x)11,color(white)(x)12,color(white)(x)13,color(white)(x)14larrcolor(red)" are the 5 integers"$

$sum of least and greatest = 10 + 14 = 24$ $"sum of least and greatest "=10+14=24$

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If the average of 5 consecutive integers is 12, what is the sum of the least and greatest of the 5 integers?

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