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Question 1150711: A bank loaned out $24,500, part of it at the rate of 9% annual interest, and the rest at 14% annual interest. The total interest earned for both loans was $3,180.00. How much was loaned at each rate?
Answer by ikleyn(52812)   (Show Source):
You can put this solution on YOUR website! .
Let x be the loaned amount at 14% interest rate.
Then the amount loaned at 9% rate is (24500-x) dollars.
The setup equation is
0.14x + 0.09*(24500-x) = 3180 dollars (the total interest amount).
From the equation
x =  = 19500.
ANSWER. $19500 was loaned at 14% and the rest, 24500-19500 = 5000 dollars, was loaned at 9%.
CHECK. 0.14*19500 + 0.09*5000 = 3180 dollars. ! Correct !
Solved.
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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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