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Three years ago, Angela's age was one year more than thrice Abel's. Four years from now, Angela's age will be two years more than twice Abel's. How old is Angela five years ago?

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Jeremiaid
The solution is very long. So, just bear with it.

Let x be the present age of Abel, and y be the present age of Angela.

x
y
       (Abel and Angela's age 3 years ago)

x-3
y-3
(Angela's age was 1 year more than 3 times Abel's)

3(x-3) + 1 = y-3   -------------------- (First Equation)

(4 years from now, Angela's age will be 2 years more than 2 times the age of Abel)

2(x+4) + 2 = y+4

(Reduce)

3(x-3) + 1 = y-3
3x-9 + 1 = y - 3
3x-9+1+3 = y
3x-5 = y ---------- (reduced first equation)

2(x+4) + 2 = y+4
2x + 8 + 2 = y+4
2x + 10 = y + 4
2x + 10 - 4 = y
2x + 6 = y ------------  (reduced second equation)

(Law of Subtraction)
             3x - 5 = y
      -      2x + 6 = y
             x -11 = 0
             x = 11
So x, the present age of Abel is 11.
Let us find y, the present age of Angela.

3x - 5 = y
3 (11) - 5 = y
33 - 5 = y
28 = y

So y, the present age of Angela is 28.

Question:    How old is Angela 5 years ago?

So, y = 28,     28 - 5 =   23

So, Angela's age 5 years ago is 23 years old.

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