SOLUTION: tommy: how old are you momma? momma? your age my age and your fathers age equal 70. tommy: how old are you papa? papa: just six times as old as you papa tommy: will i ever be h

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Question 824483: tommy: how old are you momma?
momma? your age my age and your fathers age equal 70.
tommy: how old are you papa?
papa: just six times as old as you papa
tommy: will i ever be half your age?
papa: that should happen when our three ages equal twice as much as it does today.
how old is papa momma and tommy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = momma's age now
Let +p+ = papa's age now
Let +t+ = Tommy's age now
---------------------------
(1) +t+%2B+m+%2B+p+=+70+
(2) +p+=+6t+
---------------
Let +n+ = the number of years
from now when the sum of their
ages will add up to +2%2A70+=+140+
(3) +t+%2B+n+%2B+m+%2B+n+%2B+p+%2B+n+=+140+
(3) +t+%2B+m+%2B+p+%2B+3n+=+140+
Substitute (1) into (3)
(3) +70+%2B+3n+=+140+
(3) +3n+=+70+
(3) +n+=+70%2F3+
------------------
(4) +t+%2B+70%2F3+=+%281%2F2%29%2A%28+p+%2B+70%2F3+%29+
(4) +2t+%2B+140%2F3+=+p+%2B+70%2F3+
(4) +6t+%2B+140+=+3p+%2B+70+
(4) +3p+=+6t+%2B+70+
Substitute (2) into (4)
(4) +3%2A%286t%29+=+6t+%2B+70+
(4) +18t+=+6t+%2B+70+
(4) +12t+=+70+
(4) +t+=+5+%2B+10%2F12+
Tommy is 5 yrs and 10 months
(2) +p+=+6t+
(2) +p+=+6%2A%2870%2F12%29+
(2) +p+=+35+
Papa is 35
(1) +t+%2B+m+%2B+p+=+70+
(1) +5+%2B+10%2F12+%2B+35+%2B+m+=+70+
(1) +m+=+70+-+40+-+10%2F12+
(1) +m+=+30+-+10%2F12+
(1) +m+=+29+%2B+2%2F12+
Momma is 29 and 2 months
--------------------------
check:
(2) +6%2A%28+5+%2B+10%2F12+%29+=+30+%2B+5+
(2) +30+%2B+5+=+35+
(2) +35+=+35+
-------------------
+n+=+70%2F3+
+n+=+23+%2B+4%2F12+
(3) +t+%2B+m+%2B+p+%2B+3n+=+140+
(3) +5+%2B+10%2F12+%2B+29+%2B+2%2F12+%2B+35+%2B+3%2A%28+23+%2B+4%2F12+%29+=+140+
(3) +69+%2B+1+%2B+69+%2B+1+=+140+
(3) +138+%2B+2+=+140+
(3) +140+=+140+
-----------------
(4) +t+%2B+70%2F3+=+%281%2F2%29%2A%28+p+%2B+70%2F3+%29+
(4) +5+%2B+10%2F12+%2B+23+%2B+4%2F12+=+%281%2F2%29%2A%28+35+%2B+23+%2B+4%2F12+%29+
(4) +29+%2B+2%2F12+=+%281%2F2%29%2A%28+58+%2B+4%2F12+%29+
(4) +58+%2B+4%2F12+=+58+%2B+4%2F12+
-----------------
(1) +t+%2B+m+%2B+p+=+70+
(1) +5+%2B+10%2F12+%2B+29+%2B+2%2F12+%2B+35+=+70+
(1) +34+%2B+1+%2B+35+=+70+
(1) +70+=+70+
OK
Hope I got it