SOLUTION: Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now? If x represents the son

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Question 792251: Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now?
If x represents the son's age two years ago, which expression represents his father's age three years from now?
x + 3
3x + 3
3x + 15
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let's assign the variable differently.
x = son's age now.
f = father's age now.

Two years ago, f-2=4%28x-2%29.
Simplify this: f-2=4x-8
f-4x=2-8
f-4x=-6
4x-f=6

Three years from now, f%2B3=3%28x%2B3%29.
Simplify this: f%2B3=3x%2B9
f-3x=9-3
f-3x=6
3x-f=-6

If we subtract the second equation from the first equation, we have
%284x-f%29-%283x-f%29=6-%28-6%29
x=12

The son's age NOW is 12.
The father's age NOW is+f-2=4%28x-2%29,
f=2%2B4%28x-2%29
f=2%2B4%2812-2%29
highlight%28f=42%29
But if you want an expression for f, then return to either original earlier equation and solve for f in terms of x:
f=2%2B4x-8
highlight%28f=-6%2B4x%29