You are going to invest $30,000, part at 9% and part at 14%. What is the most that can be invested at 9% in order to make at least $3000 in interest per year?
You can define a variable.
Let x be the sum invested at 9% interest.
(30000-x) will be the sum invested at 14% interest.
The interest in the first case becomes:
The interest in the second case becomes:
Total interest =
Now, equate to 3000 to find the value of x, the amount invested to 9% interest.
This gives you the greatest value invested at 9% interest to get 3000 interest per year.
If less is invested at 9%, more will be invested at 14% and you get a higher interest.
Ideally, if you want to make the most interest, put everything at 19%