SOLUTION: the sum of the present ages of Angie & her mother is 64 years. In 8 years, Angie will be three-fifths as old as her mother at that time. find the present ages of Angie & her mother

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Question 585354: the sum of the present ages of Angie & her mother is 64 years. In 8 years, Angie will be three-fifths as old as her mother at that time. find the present ages of Angie & her mother.
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of Angie = a
Present age of mother = m

Given
------
The sum of the present ages of Angie & her mother is 64 years
a+m=64
a=64-m...........(1)
In 8 years,
Angie will be = a+8
mother will be = m+8
Then
Angie will be three-fifths as old as her mother
a+8=3/5(m+8)
5(a+8)=3(m+8)
5a+40=3m+24
5a=3m+24-40
5a=3m-16...........(2)
Put the value of a from (1) to (2)
5(64-m)=3m-16
320-5m=3m-16
-5m-3m=-16-320
-8m=-336
-8m/-8=-336/-8
m=42
Put the value of m in (1)
a=64-m...........(1)
a=64-42
a=22

Present age of Angie = a = 22
Present age of mother = m = 42