If ben invests $4000 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that the interest he receives each year is 4 and 1/2% of the total amount invested

When Ben invests $4000.00 at 4%, he will have an additional $160 every year added to the 4000. Then the 4000 adds to the 4000 and the 4% is calculated.
Since Benn needs 4 and 1/2%, which is $180.00, this is the amount of money that is 4 and 1/2% of the 4000. 
So if he adds an additional $180 to the total amount of $4000 this will give him the 4 and 1/2% of his initial investment.
So we can determine that x is the amount he needs to invest.
If 0.04(4000)+0.055x=0.045(4000+x)
160+0.055x=180+0.045x
0.010x=20
x=$2000