SOLUTION: Leonard's sister Theresa was 8 years older than twice his age 3 years ago. Now Theresa is one year less than three times Leonard's age. How old is Leonard now?

Question 518403: Leonard's sister Theresa was 8 years older than twice his age 3 years ago. Now Theresa is one year less than three times Leonard's age.
How old is Leonard now?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Leonard = d
Present age of Theresa = t

Now Theresa is one year less than three times Leonard's age.
t=3d-1...............(1)
Three years ago
Leonard was = d-3
Theresa = t-3
Then
Theresa was 8 years older than twice Leonard
t-3=2(d-3)+8
t-3=2d-6+8
t-3=2d+2
t=2d+2+3
t=2d+5...............(2)
Put the value of t from (1) to (2)
3d-1=2d+5
3d-2d=5+1
d=6
Put the value of d in (1)
t=3d-1
t=3(6)-1
t=18-1
t=17
Present age of Leonard = d = 6 years old
Present age of Theresa = t = 17 years old

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