SOLUTION: 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?

Algebra.Com
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?
~~~~~~~~~~~~~~~~~~ 

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.

--------------------

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
RELATED QUESTIONS

the total interest earned after one year Php 100 000 is invested, part of 6% annual... (answered by ikleyn)
the total interest earned after one year Php 100 000 is invested, part of 6% annual... (answered by greenestamps)
Jane has $10 000 to invest. She invested part of it in a term deposit that pays 4% per... (answered by checkley71)
Kate invested $9,000 one year ago. part of the money was invested at 6% and the rest at... (answered by Mathtut)
A total of $12,000 was invested. Part of the money was invested at 4% and the rest... (answered by checkley79)
John invested $8000 for one year, part at 8% interest and the rest at 10%. If John earned (answered by josmiceli)
suppose that 18,000 is invested in two types of bonds for one year. Part of the money is... (answered by Theo)
What is the mathematical expression of this. The total interest earned after one year... (answered by Alan3354,ikleyn)
Brandon invested $20 000. He invested part of the money in a term deposit paying 4%... (answered by ikleyn,greenestamps)