## Monday, April 29, 2013

### Word Problem - Age Problem

Category: Algebra

"Published in Newark, California, USA"

Six years ago, Rosario was 4 times as old as her daughter. Ten years from now, she will be only twice as old as her
daughter. How old are they now?

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 Rosario
y = be the present age of Rosario's daughter
x - 6 = be the age of Rosario six years ago
y - 6 = be the age of Rosario's daughter six years ago
x + 10 = be the age of Rosario ten years from now
y + 10 = be the age of Rosario's daughter ten years from now.

If the first statement says, "Six years ago, Rosario was 4 times as old as her daughter." then the first working equation will be

If the second statement says, "Ten years from now, she will be only twice as old as her daughter." then the second working equation will be

Next, equate the two working equations in order to solve the age of Rosario's daughter as follows

Substitute the value of y to either of the two working equations in order to solve for the age of Rosario as follows

Therefore, in present time, Rosario is 38 years old while her daughter is 14 years old.