Question

Find two consecutive even numbers such that the difference of one-half the larger and two-fifths the smaller is equal to 38

Answer 1

EXPLANATION

The consecutive even numbers are
$370 \: and \: 372$

EXPLANATION

Let
$x$
be the first even number then, the next even number will be,

$x + 2$

The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,


$\frac{1}{2} (x + 2) - \frac{2}{5} x = 38$


We multiply through with an LCM of 10 to get,



$10 \times \frac{1}{2} (x + 2) - 10 \times \frac{2}{5} x = 38 \times 10$


This simplifies to,


$5(x + 2) - 4x = 380$


We expand the brackets to get,


$5x + 10 - 4x = 380$

We group like terms to get,


$5x - 4x = 380 - 10$



This simplifies to
$x = 370$

Therefore the next even number is is
$372$