SOLUTION: I'd really appreciate your help sir/madam. I have tried solving it many times but I am really confused about the problem. A woman has a certain amount of money invested. If she h

Question 641683: I'd really appreciate your help sir/madam.
I have tried solving it many times but I am really confused about the problem.
A woman has a certain amount of money invested. If she had $6000 more invested at a rate 1% lower, she would have the same yearly income from the investment. Furthermore, if she had $4500 less invested at a rate 1% higher, her yearly income from the investment would also be the same. How much does she have invested, and what rate is it invested?
Thanks a lot.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let be the amount (in $) of money the woman has invested.
Let be the rate at which she invested her money, written as a decimal (so 1% would be 0.01, 2% would be 0.02, and so on).
The interest she gets every year (her yearly income) is calculated as
$
An interest rate 1% lower than would be .
If the woman had invested $6000 at that lower rate, her yearly income would be
$ , and that is the same as $ , so
.
An interest rate 1% higher than would be .
If the woman had invested $4500 at that lower rate, her yearly income would be
$ , and that is the same as $ , so
.
We have a system of non-linear equations:

From there we get
--> --> --> --> --> --> --> ,
The interest rate is 7%.
Substituting into ,
--> --> --> --> --> (rounded).
The woman had $5142.86 invested.

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