SOLUTION: Six years ago, Sam was three times as old as Sue. Four years from now Sam will be twice as old as Sue will be. Find the present age of each.

Question 167906: Six years ago, Sam was three times as old as Sue. Four years from now Sam will be twice as old as Sue will be. Find the present age of each.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = Sam's present age
Let y = Sue's present age
:
Write an equation for each statement:
"Six years ago, Sam was three times as old as Sue."
x - 6 = 3(y-6)
x - 6 = 3y - 18
x = 3y - 18 + 6
x = (3y - 12)
:
" Four years from now Sam will be twice as old as Sue will be."
x + 4 = 2(y+4)
x + 4 = 2y + 8
x = 2y + 8 - 4
x = 2y + 4
:
Find the present age of each.
:
From the 1st equation, replace x with (3y-12) in the above equation:
3y - 12 = 2y + 4
3y - 2y = 4 + 12
y = 16 yrs is Sue's present age
:
Find x using the the equation: x = 2y + 4
x = 2(16) + 4
x = 36 yrs is Sam's present age
:
:
Check solution in the statement:
"Six years ago, Sam was three times as old as Sue."
36 - 6 = 3(16-6)
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