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)

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.

Define x

Let Alice be x years old 3 years ago.


Age as at 3 years ago :

Alice = x years 
Jane = 3x


Present age :

Alice = x + 3
Jane = 3x + 3


Age in two years time :

Alice = x + 3 + 2 = x + 5
Jane = 3x + 3 + 2 = 3x + 5


Construct equation :

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


Find their present age :

Alice = x + 3 = 13 + 3 = 16 years old
Jane = 3x + 3 = 13(3) + 3 = 42 years old


Alice is 16 years old and Jane is 42 years old.