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`

Step-by-step 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,



`(1)/(2) (x + 2) - (2)/(5) x = 38`


We multiply through with an LCM of 10 to get,




`10 * (1)/(2) (x + 2) - 10 * (2)/(5) x = 38 * 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`