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: $\displaystyle 9% \times x = \dfrac{9x}{100}$
The interest in the second case becomes: $\displaystyle (30000-x) \times 14% = \dfrac{14(30000 - x)}{100}$
Total interest = $\displaystyle \dfrac{9x}{100} + \dfrac{14(30000 - x)}{100}$
Now, equate to 3000 to find the value of x, the amount invested to 9% interest.
$\displaystyle \dfrac{9x}{100} + \dfrac{14(30000 - x)}{100} = 3000$
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%