EXPLANATION
The consecutive even numbers are
[tex]370 \: and \: 372[/tex]
EXPLANATION
Let
[tex]x[/tex]
be the first even number then, the next even number will be,
[tex]x + 2[/tex]
The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,
[tex] \frac{1}{2} (x + 2) - \frac{2}{5} x = 38[/tex]
We multiply through with an LCM of 10 to get,
[tex] 10 \times \frac{1}{2} (x + 2) - 10 \times \frac{2}{5} x = 38 \times 10[/tex]
This simplifies to,
[tex]5(x + 2) - 4x = 380[/tex]
We expand the brackets to get,
[tex]5x + 10 - 4x = 380[/tex]
We group like terms to get,
[tex]5x - 4x = 380 - 10[/tex]
This simplifies to
[tex]x = 370[/tex]
Therefore the next even number is is
[tex]372[/tex]
