Question 1185437: donna invested part of her money at 8% and the remainder at 10%, if she invested P400,000 and received a total of P37,000 in interest, how much did she invest each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
donna invested part of her money at 8% and the remainder at 10%, if she invested P400,000
and received a total of P37,000 in interest, how much did she invest each rate?
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Let x dollars be the amount invested at 10%.
Then the amount invested at 8% is (400000-x) dollars. (Honestly, I don't know what your "P" means and how to pronounce it . . . )
Then the equation for the total interest earned in one year is
0.1x + 0.08*(400000-x) = 37000 dollars.
From the equation
x =  = 250000.
ANSWER. P250000 invested at 10% and the rest, (400000-250000) = 150000 invested at 8%.
CHECK. 0.1*250000 + 0.08*150000 = 37000, total annual 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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
If a formal algebraic solution is not required, here is a quick an easy way to solve any 2-part mixture problem like this.
(1) All P400,000 invested at 8% would yield P32000 interest; all at 10% would yield P40000 interest; the actual amount of interest was P37000.
(2) Picture the three amounts 32000, 37000, and 40000 on a number line and observe/calculate that 37000 is 5000/8000 = 5/8 of the way from 32000 to 40000.
(3)That means 5/8 of the total was invested at the higher rate.
ANSWER: 5/8 of the P400,000, or P250,000, was invested at 10%; the other P150,000 at 8%
CHECK: .10(250000)+.08(150000)=25000+12000=37000
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