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

EXPLANATION

The consecutive even numbers are


EXPLANATION

Let

be the first even number then, the next even number will be,



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



We multiply through with an LCM of 10 to get,



This simplifies to,



We expand the brackets to get,



We group like terms to get,



This simplifies to


Therefore the next even number is is

Iagree that is the answer to the question