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Wednesday, November 19, 2014

Word Problem - Area Problems

Category: Algebra

"Published in Newark, California, USA"

In 1964, Thelma bought two lots at ₱ 9,600 each. One lot contains 40 square meters more than the other but costs ₱ 12 less per square meter. Find the area of each lot.

Solution:

The given problem is about finding the area of two lots in which Thelma bought.  The other lot has a bigger area but cheaper price. The prices of both lots are the same. Let's analyze the given word problem as follows:

Let x = be the area of Lot #1
      y = be the price of Lot #1 per square meter
      x + 40 = be the area of Lot #2
      y - 12 = be the price of Lot #2 per square meter

The working equation for Lot #1 is



The working equation for Lot #2 is




But  

Hence, the above equation becomes









By using the completing the square method, the value of x is








Since area is always a positive value, then we need to choose the positive sign. Therefore, the area of Lot #1 is




and the area of Lot #2 is 160 m² + 40 m² = 200 m²