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.
