SOLUTION: a bank loaned out 11,500, part of its interest rate of 7% annual interest, and the rest at 13% interest annual interest. the total interest earned for both loans was 865.00. how mu

Question 1155462: a bank loaned out 11,500, part of its interest rate of 7% annual interest, and the rest at 13% interest annual interest. the total interest earned for both loans was 865.00. how much was loaned at each rate?
Answer by ikleyn(52770) (Show Source): You can put this solution on YOUR website!
.


Let x = amount loaned at 13%.

The the amount loaned at 7% is  (11500-x)  dollars.


Annual interest produced by the first amount is 0.13x dollars.

Annual interest produced by the first amount is 0.07*(11500-x) dollars.


The total interest of 865 dollars is the sum of partial amounts

    0.13x + 0.07*(11500-x) = 865.


From this equation

    x =  = 1000.


ANSWER.  $1000 was loaned at 13%,  and the rest  11500-1000 = 10500 dollars were loaned at 7%.


CHECK.   0.13*1000 + 0.07*10500 = 865 dollars.   ! Precisely 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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