SOLUTION: James is now three-fifths John's age. Three years ago, he was half John's age. Three years from now, he will be two-thirds John's age. How old are they now?

Question 498510: James is now three-fifths John's age. Three years ago, he was half John's age. Three years from now, he will be two-thirds John's age. How old are they now?

Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of John = j
Present age of James = m
James is now three-fifths John's age
m=(3/5)j
m=3j/5 ........(1)
Three years ago means we have to subtract 3 from their present ages
m-3=j-3
then he was half John's age
m-3=1/2(j-3)
Multiply by 2 both sides of above equation
2(m-3)=j-3
2m-6=j-3
j-3=2m-6
j=2m-6+3
j=2m-3 ............(2)
Put the value of m from (1) to (2)
j=2m-3 ............(2)
j=2(3j/5)-3
j=6j/5 - 3
Multiply by 5 both sides of the equation
5j=6j - 15
5j-6j=-15
-j=-15
j=15
Put the value of j in (1)
m=(3/5)j
m=(3/5)(15)
m=45/5
m=9
Present age of John = 15
Present age of James = 9

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