SOLUTION: A mother is three times as old as her son. In 18 years time, she will be twice as old as her son. How old is she now?

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Question 1194288: A mother is three times as old as her son. In 18 years time, she will be twice as old as her son. How old is she now?
Found 3 solutions by ikleyn, MathLover1, MathTherapy:
Answer by ikleyn(52767) About Me  (Show Source):
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A mother is three times as old as her son. In 18 years time, she will be twice as old as her son.
How old is she now?
~~~~~~~~~~~~~~~ 

Let x be the son age; then the mother age is 3x years.


In 18 years

    3x + 18 = 2(x+18).


Simplify and find x

    3x + 18 = 2x + 36

    3x - 2x = 36 - 18

       x    =    18.


Thus the son is 18 years old;  hence, the mother is 3*18 = 54 years old.    ANSWER

Solved.

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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let mother’s age be m and son’s age s
if a mother is three times as old as her son, we have
m=3s ........eq.1
if in 18 years time, she will be twice as old as her son, we have
m%2B18=2%28s%2B18%29
m=2s%2B36-18
m=2s%2B18........eq.2
from eq.1 and eq.2 we have
3s=2s%2B18
3s-2s=18
s=18
m=3%2A18 ........eq.1
m=54
current age: mother is54 and son is 18
check their ages in 18 years time:
mother will 54%2B18=72 and son is 18%2B18=36, so she will be twice as old as her son

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
A mother is three times as old as her son. In 18 years time, she will be twice as old as her son. How old is she now? 
Let the mother's age be M
As the mother is thrice the son's age, son's age is M%2F3
We then get: 
                 3M = 2M + 54 ------- Multiplying by LCD, 3
            3M - 2M = 54
       Mother, or M, is 54 years-old