SOLUTION: 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)

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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