Question 1200867: James invested Php20,000 for one year and earned Php1470 interest. if part of the money is invested at 10%and the remainder is invested at 6%, how much is invested at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52767)   (Show Source):
You can put this solution on YOUR website! .
James invested Php20,000 for one year and earned Php1470 interest.
if part of the money is invested at 10%and the remainder is invested at 6%,
how much is invested at each rate?
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x dollars invested at 10%,
(20000-x) dollars invested at 6%.
The total annual interest equation is
0.1x + 0.06(20000-x) = 1470 dollars.
Simplify and find x
0.04x + 1200 = 1470
0.04x = 1470 - 1200
0.04x = 270
x = 270/0.04 = 6750.
ANSWER. $6750 invested at 10%; the rest 20000 - 6750 = 13250 dollars invested at 6%.
CHECK. 0.1*6750 + 0.06*13250 = 1470 dollars, total annual interest. ! correct !
Solved.
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To see many other similar solved problems using one equation in one unknown, look into the lesson
- Typical investment problems
in this site.
To see many other similar solved problems using systems of two equations in two unknowns, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The response from the other tutor shows a solution using the standard formal algebraic method.
Here is an informal method that can be used to solve any 2-part "mixture" problem like this. This method is fast and easy, especially if the numbers are "nice".
Php1470 interest on Php20,000 is an interest rate of 1470/20000 = 0.0735 = 7.35%.
The ratio in which the total was split between the two investments is exactly determined by where that 7.35% interest rate lies between the individual interest rates of 6% and 10%.
So look at the three percentages 6, 7.35, and 10 (on a number line, if it helps), and observe/calculate that the 7.35% interest rate is 1.35/4 = 135/400 = 27/80 of the way from 6% to 10%.
That means 27/80 of the total was invested at the higher rate.
20000*(27/80) = 27*(20000/80) = 27*250 = 6750
ANSWERS: Php6750 was invested at 10%; the other Php13250 was invested at 6%
CHECK: .10(6750)+.60(13250) = 675+795 = 1470
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