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2015-05-12T17:41:25+08:00

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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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