<PRE><B>Question 1197008</B>
.
A bank loaned out $19,500, part of it at the rate of 3% annual interest, 
and the rest at 8% annual interest. The total interest earned for both loans 
was $910.00. How much was loaned at each rate?
~~~~~~~~~~~~~~


&lt;pre&gt;
x = amount loaned at 8%;

(19500-x) = amount loaned at 3%.


The total annual bank&#39;s interest equation


    0.08x + 0.03*(19500-x) = 910  dollars.


Simplify and find x

    0.08x + 0.03*19500 - 0.03x = 910

    0.08x - 0.03x = 910 - 0.03*19500

         0.05x    =     325

             x    =     325/0.05 = 6500.


&lt;U&gt;ANSWER&lt;/U&gt;.  $6500 loaned at 8%  and  the rest, 19500-6500 = 13000 dollars loaned at 3%.


&lt;U&gt;CHECK&lt;/U&gt;.   0.08*6500 + 0.03*13000 = 910 dollars, total interest earned.  ! Correct !
&lt;/pre&gt;

Solved.


-------------------


It is a standard and typical problem on investments.


If you need more details,  &amp;nbsp;or if you want to see other similar problems solved by different methods, &amp;nbsp;look into the lesson 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-investment.lesson&gt;Using systems of equations to solve problems on investment&lt;/A&gt;

in this site.


You will find there different approaches &amp;nbsp;(using one equation or a system of two equations in two unknowns), &amp;nbsp;as well as 
different methods of solution to the equations &amp;nbsp;(Substitution, &amp;nbsp;Elimination).


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lesson is the part of this online textbook under the topic &amp;nbsp;&quot;&lt;U&gt;Systems of two linear equations in two unknowns&lt;/U&gt;&quot;.



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.



////////////////



The solution in the post by @ewatrrr is incorrect.



\\\\\\\\\\\\\\\\



She fixed it after seeing my post.



</PRE>