Question 1140062: seth's age is 1/4 of his friend becky now,3 yrs to come the age of seth will be 1/3 of becky.find becky's age after 3 years.(with solution plz)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE UNEXPECTED WAY:
In 3 years Becky's age will be a multiple of 3 (because Seth's age will be 1/3 of that). That means that right now Becky's age is also a multiple of 3.
Right now, Becky's age is also a multiple of 4 (because Seth's age is 1/4 of that).
As Becky's age is a multiple of 3, and a multiple of 4, and 3 and 4 are relatively prime (they do not have any common factors), Becky's age is a multiple of  .
Could Becky be 12 right now? If she were 12, Seth would be  , and in 3 years Becky and Seth would be  and  respectively. However,  is not  , so Becky is not 12 now.
Could Becky be  right now? If she were 24, Seth would be  , and in 3 years Becky and Seth would be  and  , which is indeed  of  . So Becky is 24 now, and Becky's age after 3 years will be  .
THE EXPECTED ALGEBRA SOLUTION:
We need to define a variable (or two), representing the age(s) of one or both characters in the story, either now or 3 years from now..
One way to do it:
 = Becky's age 3 years from now.
So,  = Becky's age now;
Seth's age now is  , and in 3 years Seth will be
 .
To solve that last equation, we multiply both sides times 12 to get
 .
We simplify that, in as many steps as you want.
In many steps,
 .
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