SOLUTION: If Martin was four times as old as Gary 8 years ago and if Martin will be twice as old as Gary 8 years hence, find their ages.

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Question 154831: If Martin was four times as old as Gary 8 years ago and if Martin will be twice as old as Gary 8 years hence, find their ages.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!

Let m - Martin's age now; Let g = Gary's age now
:
Write an equation for each statement:
"If Martin was four times as old as Gary 8 years ago"
(m-8) = 4(g-8)
m - 8 = 4g - 32
m - 4g = -32 + 8
m - 4g = -24
:
" and if Martin will be twice as old as Gary 8 years hence,"
(m+8) = 2(g+8)
m + 8 = 2g + 16
m - 2g = 16 - 8
m - 2g = 8
:
Subtract the 1st equation from the above equation:
m - 2g = 8
m - 4g = -24
--------------subtraction eliminates m
0 + 2g = +32
g = 32%2F2
g = 16 yrs Gary's age now
:
Use the equation; m - 2g = 8 to find m
m - 2(16) = 8
m - 32 = 8
m = 8 + 32
m = 40 yrs is Martin's age now
:
:
Check solution in the statement:
"If Martin was four times as old as Gary 8 years ago and if Martin will be twice as old as Gary 8 years hence, find their ages."
40 - 8 = 4(16-8)
and
40 + 8 = 2(16+8)