John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?

24\(\)

John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?

First thing I am going to do is change the names cause they are too confusing.

James becomes his twin sister Amy.

John is 3/4 the age of Amy. Three years ago, John was 5/7 the age of Amy. How old is Amy?

Let John's age now be J.  Three years ago his age was J-3

Let Amy's age now be A.        Three years ago her age was A-3

John is 3/4 the age of Amy.

so

\(J=\frac{3}{4}*A\\ J=\frac{3A}{4}\)

Three years ago, John was 5/7 the age of Amy.

\(J-3=\frac{5}{7}*(A-3)\\ J-3=\frac{5A-15}{7}\\ J=\frac{5A-15}{7}+3\\ \)

so

\(\frac{3A}{4}=\frac{5A-15}{7}+3\\ 28*\frac{3A}{4}=28*[\frac{5A-15}{7}+3]\\ 21A=4(5A-15)+84\\ 21A=20A-60+84\\ A=24\\ \)

Amy and therefore James, is 24 years old.