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
[tex]\frac{1}{2} \text{ of larger number } - \frac{2}{5} \text{ of smaller number } = 5[/tex]
[tex]\frac{1}{2} \times (x + 2) - \frac{2}{5} \times (x) = 5\\\\\frac{x + 2}{2} - \frac{2x}{5} = 5\\\\\frac{5(x + 2) - 2x(2)}{10} = 5\\\\5x + 10 - 4x = 50\\\\x = 50 - 10\\\\x = 40[/tex]
Thus x = 40
And x + 2 = 40 + 2 = 42
Thus the two consecutive even numbers are 40 and 42
