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Mandarinka [93]
4 years ago
15

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 p

resent ages. (4 mks)
Mathematics
2 answers:
vagabundo [1.1K]4 years ago
7 0
-----------------------------------------------
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

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


anzhelika [568]4 years ago
5 0
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.


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