SOLUTION: Sum of angie and her mother is 64 years. In 8 years angie will be (3/5) as old as her mother at that time. what are the present ages of angie and her mother?

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Question 39764: Sum of angie and her mother is 64 years. In 8 years angie will be (3/5) as old as her mother at that time. what are the present ages of angie and her mother?
Answer by vidhyak(98) About Me  (Show Source):
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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