Square, Rectangle, and Parallelogram Problems, 12

Category: Algebra, Plane Geometry

"Published in Newark, California, USA"

In 1964, Mr. Tambasen bought a rectangular lot in Bacolod City for ₱ 18,000 and spent ₱ 1,000 for building a wall around it. If the cost per square meter of the lot is ₱ 30 and the cost per linear meter of the wall is ₱ 10, find the dimensions of the lot.

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Let x = be the length of a rectangular lot

      y = be the width of a rectangular lot

The area of a rectangular lot is .

The perimeter of a rectangular lot is  .

The first working equation which is the cost of a rectangular lot is

The second working equation which is the total cost of building a wall around the rectangular lot is

Substitute the value of y to the first working equation, we have

By using the completing the square method, the value of x which is the length of a rectangular lot is

If you choose the positive sign, the value of x is

and the value of y which is the width of a rectangular lot is

If you choose the negative sign, the value of x is 

and the value of y which is the width of a rectangular lot is 

Therefore, the dimensions of a rectangular lot are 30 m by 20 m. 

Money and Investment Problems, 5

Category: Algebra

"Published in Newark, California, USA"

In 1964, Rosario invested a sum of money in the Philippine Catsup Company which gave her a return of ₱ 200 at the end of the year. Had she invested the amount in the Manila Tiles Corporation which declared a dividend of ½ % more, she would have made ₱ 70 more with an investment of ₱ 2,000 less. How much did she invest in the Philippine Catsup Company?

Solution:

The given word problem is about money and investment problem in which the money invested, annual interest rate, and annual income are involved. Let's analyze the given word problem as follows:

Let x = be the amount of money invested at Philippine Catsup Company
      y = be the annual interest rate at Philippine Catsup Company

If the word problem says "Rosario invested a sum of money in the Philippine Catsup Company which gave her a return of ₱ 200 at the end of the year.", then the working equation which is her annual income in the said company is

If the word problem says "Had she invested the amount in the Manila Tiles Corporation which declared a dividend of ½ % more, she would have made ₱ 70 more with an investment of ₱ 2,000 less.", then the working equation which is her annual income in the said company is

Next, use the two working equations in order to solve for the value of x and y which are the amount of money invested at Philippine Catsup Company and its annual interest rate, respectively.  

But  

Hence, the above equation becomes

By using the completing the square method, the value of x which is the amount of money invested at Philippine Catsup Company is 

We need to choose the positive sign since we want to get the amount of money invested at Philippine Catsup Company.

          

The annual interest rate at Philippine Catsup Company is
  

 

 

Therefore, Rosario invested ₱ 20,000 at Philippine Catsup Company with the annual interest rate of 1.0 %.