SOLUTION: Five years from now, A will be 4/5 as old as B; five years ago, he was 2/3 as old then. Find their present ages.

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Question 198526: Five years from now, A will be 4/5 as old as B; five years ago, he was 2/3 as old then. Find their present ages.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Five years from now, A will be 4/5 as old as B; five years ago,
he was 2/3 as old then.
Find their present ages.
:
Write an equation for each statement:
:
4%2F5(A+5) = (B+5)
Multiply by 5, to get rid of the denominator, simplify
4(A+5) = 5(B+5)
4A + 20 = 5B + 25
4A - 5B = -20 + 25
4A - 5B = 5
:
2%2F3(A-5) = (B-5)
Multiply by 3
2(A-5) = 3(B-5)
2A - 10 = 3b - 15
2A - 3B = -15 + 10
2A - 3B = -5
:
Multiply the above equation by -2, add to the 1st equation
-4A + 6B = +10
+4A - 5B = 5
---------------
B = 15 yrs is B's age now
then
Use 4A - 5B = 5 to find A
4A - 5(15) - 5
4A - 75 = 5
4A = 5 + 75
4A = 80
A = 80%2F4
A = 20 yrs is A's age now
:
:
Check solutions in the statement
Five years from now, A will be 4/5 as old as B;
4%2F5(20+5) = (15+5)
:
You can check solutions in the 2nd statement