SOLUTION: A mother is 20 years older then her daughter. Ten years ago the mother was twice as old as the daughter.how old are they now?

Question 501020: A mother is 20 years older then her daughter. Ten years ago the mother was twice as old as the daughter.how old are they now?
Found 2 solutions by Mr_Mathman, Maths68:
Answer by Mr_Mathman(5) (Show Source): You can put this solution on YOUR website!
Mom's age is 20+x
Mom's age ten years ago is 20+x-10 = 10+x
Twice the daughter's age ten years ago is 2(x-10)
hence
10+x = 2(x-10) = 2x-20
10+x = 2x-20 add 20 to both sides of the eqn.
30+x = 2x subtract x from both sides of the eqn
30 = x
sothe daughter is 30 years old now and the Mom is 30+20 = 50 years old now
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of mother = m
Present age of daughter = d
Mother is 20 years older then her daughter means if we add 20 years to daughter's age both will be of equal age
m=d+20 .........(1)
Ten years ago means we have to subtract 10 from their present ages
m-10=d-10
then
the mother was twice as old as the daughter
m-10=2(d-10)
m-10=2d-20
m=2d-20+10
m=2d-10...........(2)
Plug in the value of m from (1) to (2)
m=2d-10
d+20=2d-10
d-2d=-10-20
-d=-30
Multiply by (-1) both sides of the equation
(-1)(-d)=(-1)(-30)
d=30
Now plug in the value of d in (1)
m=d+20 .........(1)
m=30+20
m=50
Mother is 50 and daughter is 30 years old

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