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How can I solve this using 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?

Sagot :

Linear Equation:

Representation:
x = Investment A
y = Investment B

Equation 1:  Sum of Investments

x + y = 400,000

Equation 2: Sum of Interest on Investments A and B
0.03x + 0.07y = 16,000

Solve using Substitution:
x + y = 400,000
y = 4000,000 - x

Solve for x (Investment A):
Substitute 400,000 - x for y in Equation 2:
0.03x + 0.07y = 16,000
0.03 x + 0.07 (400,000 - x) = 16,000
0.03x - 0.07x + 28,000 = 16,000
-0.04x = 16,000 - 28,000
-0.04x = - 12,000
-0.04x/0.04 = -12,000 / -0.04
x = 300,000      

Investment A (x) = 300,000 pesos

Solve for y (Investment B):
Substitute 300,000 for x in Equation 1:
x + y = 400,000
300,000 + y = 400,000
y = 400,000 - 300,000
y = 100,000

Investment B (y) = 100,000 pesos

Interest on each investment:
Investment A:
0.03 (x) = 0.03 (300,000) = 9,000 pesos

Investment B:
0.07 (y) = 0.07 (100,00) = 7,000 pesos

Sum of interests on investments:
9,000 + 7,000 = 16,000
16,000 = 16,000

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