Question 1141702: You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 6.1 percent interest. If the two accounts pay 3 percent and 7 percent interest, how much should you invest in each account?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52784)   (Show Source):
You can put this solution on YOUR website! .
Let x dollars be your investment at 7%;
then the investment at 3% is the rest (1000-x) dollars.
The total interest equation is
0.07x + 0.03*(1000-x) = 0.061*1000.
Express x and calculate
x =  = 775.
ANSWER. $700 is the 7% investment; the rest, (1000-775) = 225 dollars is the 3% investment.
CHECK. 0.07*775 + 0.03*225 = 61 dollars = 6.1% of $1000. ! Correct !
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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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the standard algebraic solution method shown by the other tutor.
(1) Picture the three percentages 3, 6.1, and 7 on a number line.
(2) Imagine walking from 3 towards 7 on the number line, stopping when you reach 6.1. What fraction of the distance have you walked?
(3) That fraction is the fraction of the total that must be invested at the higher rate.
(31/40)*$1000 = 31*$25 = $775.
ANSWER: $775 at 7%; $225 at 3%.
Note that split gives you an average interest rate of EXACTLY 6.1%. In reality, the requirement would be to have an average of AT LEAST 6.1%; that would mean the amount invested at the higher rate would have to be AT LEAST $775.
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