How do you find two consecutive even integers such that twice the smaller is 26 less than 3 times the larger?

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Answer 1 · 2016-10-30T10:00:10

The numbers are $20 and 22$ $20 and 22$

First use a variable to define the two unknown numbers.

Let the smaller even number be $x$ $x$
The larger number is $x + 2$ $x+2$

"Twice the smaller": $2 x$ $2x$

"3 times the larger": $3 (x + 2)$ $3(x+2)$

These two numbers differ by 26.

"Bigger value - smaller value " = $26$ $26$

$3 (x + 2) - 2 x = 26 \leftarrow$ $3(x+2) - 2x = 26" "larr$ here is the equation. Solve it.

$3 x + 6 - 2 x = 26$ $3x+6 -2x = 26$

$x = 26 - 6$ $x = 26-6$

$x = 20$ $x = 20$

$20$ $20$ is the smaller number, The larger is $22$ $22$

Check:

$3 \times 22 = 66 and 2 \times 2 = 40$ $3xx22 = 66" and "2 xx 2 = 40$

$66 - 40 = 26$ $66-40 =26$