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Question 1197008: 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?
Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
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?
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x = amount loaned at 8%;
(19500-x) = amount loaned at 3%.
The total annual bank'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.
ANSWER. $6500 loaned at 8% and the rest, 19500-6500 = 13000 dollars loaned at 3%.
CHECK. 0.08*6500 + 0.03*13000 = 910 dollars, total interest earned. ! 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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The solution in the post by @ewatrrr is incorrect.
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She fixed it after seeing my post.
Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website!
Hi
A bank loaned out $19,500, part of it at the rate of 3% annual interest,
and the rest 'x' at 8% annual interest.
The total interest earned for both loans was $910.00.
How much was loaned at each rate?
NOte: Assigned x to the largest interest rate for ease of set up.
.08x + .03(19500 - x) = 910
.05x = 
x = (910-585)/.05 = $6500 at 8%, $13,000 at .03%
.08*$6500 + .03*$13000 = $910 checks
Wish You the Best in your Studies.
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