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Sunday, August 18, 2013

Word Problem - Age Problem, 2

Category: Algebra

"Published in Newark, California, USA"

Mr. Manalang is 36 years old. His age is twice the sum of the ages of his two sons. How are old are his sons now, if the sum of the squares of their ages, 2 years ago, was 2 less than thrice Mr. Manalang's age then?

Solution:

The given word problem is about age problem where you need to solve for the age of a person or people. Let's analyze the given word problem above as follows: 

Let x = be the present age of Mr. Manalang's first son
      y = be the present age of Mr. Manalang's second son

If the first statement says, "Mr. Manalang is 36 years old. His age is twice the sum of the ages of his two sons.", then the working equation will be



If the second statement says, ".....if the sum of the squares of their ages, 2 years ago, was 2 less than thrice Mr. Manalang's age then?", then the working equation will be

   



If the first equation is 



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




Expand the above equation and solve for the value of x, we have







Equate each factor to zero, if





then the value of y will be equal to






And if,



then the value of y will be equal to




Therefore, the age of Mr. Manalang's sons are 10 years old and 8 years old