How can I solve this in linear equations in two variables

Mr. Salonga has two investments. His total investment is Php 400,000.
Annually, he receives 3% interest on one investment and 7%
interest on the other. The total interest that Mr. Salonga receives
in a year is Php 16,000.

a. How much money does Mr. Salonga have in each investment?
b. In which investment did Mr. Salonga earn more?
c. Suppose you were Mr. Salonga, in which investment will you
place more money? Why?

1

Answers

2015-12-10T08:43:17+08:00

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First we have to translate this into mathematical expression.
Let  x = first investment
       y = second investment

Total investment of Mr. Salonga
(1) x + y = 400,000

Interest of the first investment in one year @ 3% or 0.03
A = x(0.03)(1) = 0.03x

Interest of the second investment in one year @ 7% or 0.07
B = y(0.07)(1) = 0.07y

Total interest of Mr. Salonga
                    A + B = 16,000
 (2)  0.03x + 0.07y = 16,000

We have now two equations which can be solved by elimination method
(1) x + y = 400,000
 (2) 100 (0.03x + 0.07y) = (16,000)100
 (2) 3x + 7y = 1,600,000

(1) x + y = 400,000
(2) 3x + 7y = 1,600,000
Multply (1) with -3
(1) (-3)(x + y) = (400,000)(-3)
     -3x -3y = -1,200,000
Add the two equations
     -3x -3y = -1,200,000
      3x + 7y = 1,600,000
____________________
           4y = 400,000
           y = 100,000

Substitute y = 100,000 to (1) to solve for x
(1) x + y = 400,000
     x + 100,000 = 400,000
     x = 400,000 - 100,000
     x = 300,000

a. Therefore, the two investments of Mr. Salonga are Php 300,000 and Php100,000

Let's check which of the two investment earn more

Investment at 3% interest
A = 0.03x
A = (0.03)(300,000)
A = 9,000
Investment at 7% interest
B = 0.07y
B = (0.07)(100,000)
B = 7,000

b. Therefore, the investment of Php300,000 earn more than the investment of Php100,000

c. If I were Mr.Salonga, I will place more money with 7% interest because it gains more interest than 3%.
Example if 300,000 will be invested with 7% = (0.07)(300,000) = 21,000
As you can see, you will gain 21,000 at 7% interest compare to 3% interest which interest is only 9,000.
              













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