Question 1185278: A bank loaned out $19,500, part of it at the rate of 4% annual interest, and the rest at 5% annual interest. The total interest earned for both loans was $940.00. How much was loaned at each rate
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
A bank loaned out $19,500, part of it at the rate of 4% annual interest, and the rest at 5% annual interest.
The total interest earned for both loans was $940.00. How much was loaned at each rate
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x = amount loaned at 5%;
(19500-x) = amount loaned at 4%.
The total annual bank's interest equation
0.05x + 0.04*(19500-x) = 940 dollars.
From the equation
x =  = 16000.
ANSWER. $16000 loaned at 5%; the rest, 19500-16000 = 3500 loaned at 4%.
CHECK. 0.05*16000 + 0.04*3500 = 940 dollars, annual bank's interest. ! 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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
If you need to solve 2-part "mixture" problems like this often, and a formal algebraic solution is not required, here is a quick and easy way to solve this kind of problem.
(1) All $19,500 at 4% would yield $780 interest; all at 5% would yield $975 interest. The actual interest was $940.
(2) Picture the three interest amounts on a number line -- 780, 940, and 975 -- and observe/calculate that 940 is 160/195 of the way from 780 to 975. That means 160/195 of the total amount was invested at the higher rate.
(3) The numbers work out very nicely in this example; 160/195 of $19,500 is $16,000.
ANSWER: $16,000 was invested at 5%; the other $3,500 at 4%.
CHECK: .05(16000)+.04(3500)= 800+140=940
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