SOLUTION: Ronald, Mark and Paula are three children in the same family. Paula is three times Mark's age. In two years, she will be twice the age Ronald will be at that time. Ronald is one ye

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Question 505650: Ronald, Mark and Paula are three children in the same family. Paula is three times Mark's age. In two years, she will be twice the age Ronald will be at that time. Ronald is one year older than Mark. How old is each child
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of Ronald = r
Present age of Paula = p
Present age of Mark = m
Paula is three times Mark's age
p=3m .........(1)
In two years means we have to add 2 in their present ages
p+2=r+2
then
Paula will be twice the age Ronald will be at that time
p+2=2(r+2)
p+2=2r+4
p=2r+4-2
p=2r+2 ............(2)
Ronald is one year older than Mark means if we subtract to 1 from the Ronald's age then both Ronald and Mark will of equal age
m=r-1 ............(3)
Put the value of m from (3) to (1)
p=3m .........(1)
p=3(r-1)
p=3r-3 ............(4)
Put the value of p from (4) to (2)
p=2r+2 ............(2)
3r-3=2r+2
3r-2r=2+3
r=5
Put the value of r in (3)
m=r-1 ............(3)
m=5-1
m=4
Put the value of m in (1)
p=3m .........(1)
p=3(4)
p=12
Present age of Ronald = r = 5
Present age of Paula = p = 12
Present age of Mark = m = 4