SOLUTION: Anita is 3/4 the age of Judy. 4 years ago, she was 2/3s the age of Judy. How old is each?

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Question 973289: Anita is 3/4 the age of Judy. 4 years ago, she was 2/3s the age of Judy. How old is each?
Answer by macston(5194) About Me  (Show Source):
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J=Judy's age; A=Anita's age=(3/4)J=0.75J
A-4yrs=(2/3)(J-4yrs) Substitute for A
(3/4)J-4yrs=(2/3)(J-4yrs) Multiply each side by 3/2.
(9/8)J-6yrs=J-4yrs Add 5 yrs to each side.
(9/8)J=J+2yrs Subtract J from each side.
(1/8)J=2yrs Multiply each side by 8.
J=16yrs ANSWER 1: Judy is 16 years old.
A=(3/4)J=(3/4)16yrs=12 yrs ANSWER 2: Anita is 12 years old.
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CHECK:
A-4yrs=(2/3)(J-4yrs)
12yrs-4yrs=(2/3)(16yrs-4yrs)
8yrs=(2/3)(12yrs)
8yrs=8yrs