Question 39764
Let Angie's age be A and her mother's age be M


Sum of angie and her mother is 64 years

A + M = 64 ------eq 1


In 8 years angie will be (3/5) as old as her mother at that time. 

(A + 8) = (3/5)(M + 8)

5(A  + 8) =  3(M + 8 )
5A + 40 = 3M + 24
5A - 3M = 24 - 40
5A - 3M = -16  ------ eq 2


Multiple eq1 by 3 and add with eq 2 


3A + 3M = 192
5A - 3M = -16
-------------------------------
8A  =  176

A = 176/8  = 22


Substitute A = 22 in eq1


A + M = 64 
22 + M = 64 
M = 64 - 22
M = 42


Angie's  age is 22 and her mother's age is 42