The greater of 2 consecutive even integers is 58 less than three times the smaller, what are the numbers?

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The greater of 2 consecutive even integers is 58 less than three times the smaller, what are the numbers?

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Answer 1 · 2015-06-03T09:42:19

Two consecutive even integers can be represented as $x and x + 2$ $color(purple)( x and x+2$
(as the difference between two even integers eg : 8 - 6 = 2 )

The greater of the two = $x + 2$ $color(blue)(x+2$
Three times the smaller integer = $3 \times (x) = 3 x$ $3xxcolor(blue)((x) = 3x$

as per the condition of the question:
$x + 2 = 3 x - 58$ $x+2 = 3x - 58$
now solving the equation:
$2 + 58 = 3 x - x$ $2+58 = 3x-x$
$2 x = 60, x = 30$ $2x = 60 , color(blue)(x = 30$

and $x + 2 = 32$ $color(blue)(x+2= 32$
so the numbers are $30 and 32$ $color(blue)(30 and 32$

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The greater of 2 consecutive even integers is 58 less than three times the smaller, what are the numbers?

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