|
Question 1135999: Phyllis invested
35000
35000
dollars, a portion earning a simple interest rate of
4
4
percent per year and the rest earning a rate of
6
6
percent per year. After one year the total interest earned on these investments was
1800
1800
dollars. How much money did she invest at each rate
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
0.04*x + 0.06*(35000-x) = 1800.
Solve for x, which is an unknown amount at 4%.
Had
your
post
was
better
formatted,
I would provide more detailed solution.
------------------
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(13198)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the standard algebraic solution method suggested by the other tutor.
This problem is essentially a mixture problem -- you are mixing investments at 4% and 6% and getting an overall percentage return somewhere between 4% and 6%.
This method for solving mixture problems is based on the fact that how the investment is split between the two percentages exactly determines the overall interest rate.
(1) $35000 all at 4% would provide $1400 interest; all at 6% would provide $2100 interest.
(2) The actual amount of interest, $1800, is 4/7 of the way from $1400 to $2100. (2100-1400 = 700; 1800-1400 = 400; 400/700 = 4/7)
(3) That means 4/7 of the total was invested at the higher rate.
ANSWER: 4/7 of $35,000 = $20,000 at 6%; 3/7 of $35,000 = $15,000 at 4%.
CHECK: .06(20,000)+.04(15,000) = 1200+600 = 1800
|
|
|
| |
