SOLUTION: Sum of the present ages of Angie and her moether is 64 years. In eight years Angie will be three-fifths as old as her moether at that time. Find the present ages of Angie and her m

Question 83463This question is from textbook
: Sum of the present ages of Angie and her moether is 64 years. In eight years Angie will be three-fifths as old as her moether at that time. Find the present ages of Angie and her mother. This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let A = Angie's present age; M = Mom's present age
:
Write an equation for each sentence:
:
"Sum of the present ages of Angie and her mother is 64 years."
A + M = 64
A = 64 - M; use for substitution later
:
"In eight years Angie will be three-fifths as old as her mother at that time."
(A + 8) = .6(M + 8)
A + 8 = .6M + 4.8
A = .6M + 4.8 - 8
A = .6M - 3.2
:
Find the present ages of Angie and her mother.
Substitute (64-M) for A in the above equation:
64 - M = .6M - 3.2
-M - .6M = - 3.2 - 64
-1.6M = -67.2
M = -67.2/-1.6
M = +42 yrs old
:
Find A: 64 - 42 = 22 yrs old
:
Check using the statement:
"In eight years Angie will be three-fifths as old as her mother at that time."
(22 + 8) = .6(42 + 8)
30 = .6(50) proves our solutions
:

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