Question 1138266: Isabella has twice as much money invested at 4% as she has invested at 3%, and she has $500 more invested at 5% than she has at 3%. If the annual income from these three investments is $2025, how much does she have invested at 4%?
Answer by ikleyn(52812)   (Show Source):
You can put this solution on YOUR website! .
Let x be the amount invested at 3%.
Then the amount invested at 4% is 2x dollars,
and the amount invested at 5% is (x+500) dollars.
From the condition, the total interest equation is
0.03x + 0.04(2x) + 0.05*(x+500) = 2025.
Simplify and solve for x
0.03x + 0.04*2 + 0.05 + 0.05*500 = 2025
x =  = 12500.
So, $12500 was invested at 3% and twice of it, $25000 was invested at 4%.
Answer. $25000 was invested at 4%.
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It is a standard and typical problem on investments.
If you need more details, or if you want to see other similar problems solved by different methods, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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