John is 3/4 the age of James. Three years ago, John was 5/7 the age of James. How old is James?
+118687 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.
