Answer: he should invest $15000 at 6% and $5000 at 4%
Step-by-step explanation:
Let x represent the part of his money that he should invest at 6%.
Let y represent the part of his money that he should invest at 4%.
Paul has $20000 to invest. He can invest part of his money at 6% and the rest at 4%. It means that
x + y = 20000
The interest that he would earn on the amount invested at 6% after 1 year is
6/100 × x = 0.06x
The interest that he would earn on the amount invested at 4% after 1 year is
4/100 × y = 0.04y
if he wants to get a total of $1100 interest on his $20000, it means that
0.06x + 0.04y = 1100- - - - - - - - - 1
Substituting x = 20000 - y into equation 1, it becomes
0.06(20000 - y) + 0.04y = 1100
1200 - 0.06y + 0.04y = 1100
- 0.06y + 0.04y = 1100 - 1200
- 0.02y = - 100
y = - 100/-0.02
y = 5000
x = 20000 - y = 20000 - 5000
x = 15000
