SOLUTION: John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. What are the present ages of John and Sally?

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Question 62371: John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. What are the present ages of John and Sally?
Answer by joyofmath(189) About Me  (Show Source):
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John's present age is three-fourths of Sally's present age. In five years, John's age will be four-fifths of Sarah's age at that time. What are the present ages of John and Sally?
The two equations are:
J=%283%2F4%29S.
J%2B5=%284%2F5%29%28S%2B5%29.
Replace J with (3/4)S in the 2nd equation:
%283%2F4%29S%2B5=%284%2F5%29%28S%2B5%29.
Multiply both sides of the equation by 20 to get rid of the fractions:
15S%2B100=16%28S%2B5%29.
Or, 15S%2B100=16S%2B80.
Or, 100=S%2B80.
So, S=20.
Sally is 20 years old. John is 3/4 of Sally's age so John is 15.
Verification:
In 5 years Sally will be 25 and John will be 20 which is indeed four-fifth's of Sally's age in 5 years.