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Question 1137672: A bank loaned out $7,000, part of it at the rate of 12% annual interest, and the rest at 5% annual interest. The total interest earned for both loans was $455.00. How much was loaned at each rate?
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount loaned at 12%, in dollars.
Then the amount loaned at 5% is the rest (7000-x) dollars.
The interest from the 12% amount is 0.12*x dollars.
The interest from the 5% amount is 0.05*(7000-x) dollars.
Your equation is
interest + interest = total interest, or
0.12*x + 0.05*(7000-x) = 455 dollars.
From the equation, express x and calculate the answer
x =  = 1500.
Answer. The amount loaned at 12% is $1500; the rest $7000-$1500 = $5500 is the amount loaned at 5%.
Check. 0.12*1500 + 0.05*5500 = 455 dollars. ! Correct !
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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.
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