Question

3. Three years ago, Jane was three times as old as Alice. In two years time, the sum of their ages will be 62. Determine their present ages. (4 mks)

Answer 1

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Define x
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Let Alice be x years old 3 years ago.

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Age as at 3 years ago :
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Alice = x years 
Jane = 3x

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Present age :
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Alice = x + 3
Jane = 3x + 3

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Age in two years time :
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Alice = x + 3 + 2 = x + 5
Jane = 3x + 3 + 2 = 3x + 5

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Construct equation :
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In two years time, the sum of their age will be 62:
x + 5 + 3x + 5 = 62
4x + 10 = 62
4x = 62 - 10
4x = 52
x = 13

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Find their present age :
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Alice = x + 3 = 13 + 3 = 16 years old
Jane = 3x + 3 = 13(3) + 3 = 42 years old

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Answer: Alice is 16 years old and Jane is 42 years old.
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Answer 2

3 yrs ago:

Alice - x 
Jane - 3x 

Fast forward 2 years... 1 year ago: 

Sum of their ages = 62


Equation to solve: x + 3x = 62 
                                4x = 62 
                               -----  -----
                                 4      4
 
                                 x = 15.5 

From this, we can deterime that Alice is 15 1/2 years old. 

Then, plug in 15.5 for x in 3x to find Jane's age. 

15.5 × 3 = 46.5

From this, we can determine that Jane is 46 1/2 years old. 


I hope this helps you to understand this problem better.