Answer:
The correct option is 2. The consecutive even numbers are 40 and 42.
Step-by-step explanation:
Let the two consecutive even numbers be x and x+2.
It is given that the difference of one-half the larger number and two-fifths the smaller number is equal to five.
[tex]\frac{1}{2}(x+2)-\frac{2}{5}(x)=5[/tex]
[tex]\frac{x+2}{2}-\frac{2x}{5}=5[/tex]
[tex]\frac{5x+10-4x}{10}=5[/tex]
[tex]x+10=50[/tex]
[tex]x=50-10[/tex]
[tex]x=40[/tex]
The value of x is 40. Therefore the two consecutive even numbers are 40 and 42.
Option 2 is correct.
