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Question 1123045: Linda Smaoke invests a total of $ 10,000 in two savings accounts. One account pays 6 % interest, and the other, 7 %. Find the amount placed in each account if the accounts receive a total of $ 610 in interest after 1 year. Use interest=principalXrateXtime
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52873)   (Show Source):
You can put this solution on YOUR website! .
Let x= the amount invested at 7%.
The the rest, 10000-x dollars is the amount invested at 6%.
The interest equation is
0.07x + 0.06*(10000-x) = 610 dollars.
Simplify and solve for x.
Then evaluate 10000 -x.
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It is a typical and standard problem on investment.
To see many other similar solved problems on investment, 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(13208)  (Show Source):
You can put this solution on YOUR website!
Here is a method for solving problems like this which, if you understand it, will get you to the answer much faster and with far less work than the traditional algebraic approach shown by the other tutor.
The $610 interest on $10,000 means the overall interest rate was 6.1%.
Where that 6.1% lies between 6% and 7% exactly determines how the money is split between the two accounts.
There are many variations on how you can get the answer using this method. For me, this is the easiest:
6.1% is 1/10 of the way from 6% to 7%; that means 1/10 of the money was invested at the higher rate.
1/10 of $10,000 is $1000. So
Answer: $9000 at 6%; $1000 at 7%.
CHECK: 6% of $9000 = $540; 7% of $1000 = 70; $540+$70 = $610
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