Question 352026: 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?
Found 2 solutions by checkley77, nyc_function:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! .14X+.09(30,000-X)>3,000
.14X+2,700-.08X>3,000
.06X>3,000-2,700
.06X>300
X>300/.06
X>5,000 AMOUNT INVESTED @ 14%.
30,000-5,000=25,000 AMOUNT INVESTED @ 9%.
PROOF:
LET THE 9% INVESTMENT BE $24,999 & THE INVESTMENT @ 14% BE 5,001.
.14*5,001+.09*24,999>3,000
700.14+2,249.91>3.000
2950.05<3,000 SHOWS THAT $1 LESS INVESTED @ 9% RESULTS IN LESS THAN $3,000 IN INTEREST.
Answer by nyc_function(2741)  (Show Source):
You can put this solution on YOUR website! 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: 9
The interest in the second case becomes: (30000 - x) times 14.
Total interest = (9x/100) + 14(3000 - x)/100
Now, equate to 3000 to find the value of x, the amount invested to 9% interest.
(9x/100) + 14(3000 - 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 percent.
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