SOLUTION: Meenakshi: ‘How old are you ,Mom’ Mom: ‘Let me think, Meenakshi, well our three ages add up exactly seventy years’ Meenakshi: That it a lot, is not it? And how old are you Dad?

Algebra ->  Equations -> SOLUTION: Meenakshi: ‘How old are you ,Mom’ Mom: ‘Let me think, Meenakshi, well our three ages add up exactly seventy years’ Meenakshi: That it a lot, is not it? And how old are you Dad?      Log On


   



Question 983103: Meenakshi: ‘How old are you ,Mom’
Mom: ‘Let me think, Meenakshi, well our three ages add up exactly seventy years’
Meenakshi: That it a lot, is not it? And how old are you Dad?
Dad: Just Six times as old as you, my daughter.
Meenu: Shall I ever be half as old as you, Dad?
Dad: ‘Yes , Meenakshi, when that happens our three ages will add up to exactly twice as much as today’
Meenakshi: ‘ And supposing I was born before you Dad, and Mom has forgot all about it , and had not been at home when I came, and supposing-----‘
Mom: ‘Supposing, Meenakshi, we talk about that in bed. Come along, Vamshi you will have a head ache’
Now if Meenakshi has been some years older she might have calculated the exact ages of her parents from the information they had given her. can you find out the exact age of her MOM.?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Mom's age now
Let +b+ = Meenakshi's age now
Let +c+ = Dad's age now
--------------------------------
given:
(1) +a+%2B+b+%2B+c+=+70+
(2) +c+=+6b+
----------------------
The amount you add to each of their ages
when the sum of their ages is +2%2A70+=+140+
is +70%2F3+=+23.333+
Now I have the equation:
+a+%2B+23.333+%2B+b+%2B+23.333+%2B+c+%2B+23.333+=+70+%2B+70+
I can now say:
+b+%2B+23.333+=+%281%2F2%29%2A%28+c+%2B+23.333+%29+
Plug (2) into this equation
+b+%2B+23.333+=+%281%2F2%29%2A%28+6b+%2B+23.333+%29+
+2b+%2B+46.667+=+6b+%2B+23.333+
+4b+=+23.333+
+b+=+5.8333+
and
(2) +c+=+6b+
(2) +c+=+35+
and
(1) +a+%2B+b+%2B+c+=+70+
(1) +a+%2B+5.8333+%2B+35+=+70+
(1) +a+=+70+-+40.8333+
(1) +a+=+29.1667+
------------------------------
+.1667%2A12+=+2+
+.8333%2A12+=+10+
--------------------
Mom is 29 and 2 months
----------------------
check answer:
Menakshi's age is 5 yrs 10 months
Dad's age is 35
----------------
(1) +a+%2B+b+%2B+c+=+70+
(1) +29.1667+%2B+5.8333+%2B+35+=+70+
(1) +35+%2B+35+=+70+
---------------------
(2) +c+=+6b+
(2) +35+=+6%2A5.8333+
(2) +35+=+35+
OK