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Question 1143754: you invested $29000 in two accounts paying 6 % and 8 % annual interest, respectively.
If the total interest earned for the year was $ 2040 comma how much was invested at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount at 8%, in dollars.
Then the amount at 6% is the rest (29000-x) dollars.
The interest from the 8% amount is 0.08*x dollars.
The interest from the 6% amount is 0.06*(19000-x) dollars.
Your equation is
interest + interest = total interest, or
0.08*x + 0.06*(29000-x) = 2040 dollars.
From the equation, express x and calculate the answer
x =  = 15000.
Answer. The amount at 8% is $15000; the rest $29000-$15000 = $14000 is the amount at 6%.
Check. 0.06*14000 + 0.08*15000 = 2040 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.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
Here is a non-algebraic method for solving this kind of problem, treating it as a mixture problem.
$29000 all invested at 6% would yield $1740 interest; all invested at 8% would yield $2320 interest.
The way the money is split between the two investments is exactly determined by where the actual amount of interest lies between those two amounts.
So consider the three interest amounts on a number line: 1740, 2040, and 2320.
(1) The difference between $1740 and $2320 is $580; the difference between $1740 and $2040 is $300.
(2) So we can say that the actual amount of interest is 300/580 = 30/58 = 15/29 of the way from $1740 to $2320.
(3) That means 15/29 of the total was invested at the higher rate.
ANSWER: (15/29) of $29,000, or $15,000 at 8%; the rest, $14,000, at 6%.
CHECK: .08(15000)+.06(14000) = 1200+840 = 2040
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