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

Oct 30, 2016

The numbers are $20 \mathmr{and} 22$

Explanation:

First use a variable to define the two unknown numbers.

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

"Twice the smaller": $2 x$

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

These two numbers differ by 26.

"Bigger value - smaller value " = $26$

$3 \left(x + 2\right) - 2 x = 26 \text{ } \leftarrow$ here is the equation. Solve it.

$3 x + 6 - 2 x = 26$

$x = 26 - 6$

$x = 20$

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

Check:

$3 \times 22 = 66 \text{ and } 2 \times 2 = 40$

$66 - 40 = 26$