Question

Find two consecutive even numbers such that the difference of one-half the larger number and two-fifths the smaller number is equal to five. 38 and 40 40 and 42 42 and 44

Answer 1

The two consecutive even numbers are 40 and 42

Solution:

Let the two consecutive even numbers be x and x + 2

Let "x" be the smaller number and "x + 2" be the larger number

Given that difference of one-half the larger number and two-fifths the smaller number is equal to five

So we can frame a equation as,

one-half the larger number - two-fifths the smaller number = 5

`(1)/(2) \text{ of larger number } - (2)/(5) \text{ of smaller number } = 5`

`(1)/(2) * (x + 2) - (2)/(5) * (x) = 5\\\\(x + 2)/(2) - (2x)/(5) = 5\\\\(5(x + 2) - 2x(2))/(10) = 5\\\\5x + 10 - 4x = 50\\\\x = 50 - 10\\\\x = 40`

Thus x = 40

And x + 2 = 40 + 2 = 42

Thus the two consecutive even numbers are 40 and 42