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Saturday, March 9, 2013

Money - Investment Problem, 3

Category: Algebra

"Published in Newark, California, USA"

Noel invested ₱ 25,000 in 2 business ventures one earning 6% and the other 8% at the end of the year. If his proceeds amounted to ₱ 1,900.00, how much did he invest in each?

Solution:

The given word problem is about money and investment problem. Let's analyze the given word problem as follows

Let x = amount of money invested in business A
      y = amount of money invested in business B
      ₱ 25,000.00 = total amount of money invested
      6% = annual interest in business A
      8% = annual interest in business B
      0.06x = annual earning in business A
      0.08y = annual earning in business B
      ₱ 1,900.00 = annual total earning

From the word statement, "Noel invested ₱ 25,000 in 2 business ventures....", then the working equation will be

                                    x + y = 25,000

From the word statement, "If his proceeds amounted to ₱ 1,900.00.....", then the working equation will be

                                    0.06x + 0.08y = 1,900

We can solve for the value of x and y using the two equations, two unknowns. Consider the first equation

                                    + y = 25,000

                            or           y = 25,000 - x

Substitute the value of y to the second equation, we have

                                    0.06x + 0.08y = 1,900

                    0.06x + 0.08(25,000 - x) = 1,900

                         0.06x + 2,000 - 0.08x = 1,900

                                              - 0.02x = 1,900 - 2,000

                                              - 0.02x = - 100

                                                       x = 5,000

Substitute the value of x to the first equation, we have

                                     y = 25,000 - x

                                     y = 25,000 - 5,000

                                     y = 20,000

Therefore, Noel invested ₱ 5,000.00 in business A and ₱ 20,000.00 in business B.

Note: The monetary sign, ₱ means Philippine Pesos and the word problem was in 1964.