What are three consecutive even integers such that the sum of the first and twice the second is 20 more than the third?

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What are three consecutive even integers such that the sum of the first and twice the second is 20 more than the third?

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Answer 1 · 2016-04-23T05:27:02

10, 12, 14

Explanation:

Let $x$ $x$ be the smallest of the 3 integers
$\Rightarrow$ $=>$ the second integer is $x + 2$ $x + 2$
$\Rightarrow$ $=>$ the largest integer is $x + 4$ $x + 4$

$x + 2 (x + 2) = x + 4 + 20$ $x + 2(x + 2) = x + 4 + 20$
$\Rightarrow x + 2 x + 4 = x + 24$ $=> x + 2x + 4 = x + 24$
$\Rightarrow 3 x + 4 = x + 24$ $=> 3x + 4 = x + 24$
$\Rightarrow 2 x = 20$ $=> 2x = 20$ => x = 10#

$\Rightarrow x + 2 = 12$ $=> x + 2 = 12$
$\Rightarrow x + 4 = 14$ $=> x + 4 = 14$

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What are three consecutive even integers such that the sum of the first and twice the second is 20 more than the third?

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