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 at present?

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Question 131956: 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 at present?
Found 2 solutions by stanbon, ptaylor:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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 at present?
--------------------
2 years ago DATA:
Son's age was "x"
Father's age was "4x"
-------------------------
Three years from now DATA
Son's age will be "x+5"
Father will be "4x+5"
-------------------------
EQUATION:
4x+5 = 3(x+5)
4x+5 = 3x+15
x = 10
Son's age NOW = x+2 = 12 yrs old
--------------
Father's age NOW = 4x+2 = 42 yrs old
======================
Cheers,
Stan H.

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!

Let x=son's age now
And let y=father's age now
Now we are told that:
4(x-2)=y-2------------------------eq1
We are also told:
3(x+3)=y+3-----------------------------eq2
subtract eq1 from eq2 and we get:
3(x+3)-4(x-2)=5 get rid of parens
3x+9-4x+8=5 or
-x+17=5 subtract 17 from both sides
-x+17-17=5-17 collect like terms
-x=-12 divide both sides by -1
x=12------------------------------son's age now
substitute x=12 into eq1
4(12-2)=y-2
40=y-2 add 2 to each side
40+2=y-2+2
y=42----------------------father's age now
CK
4(12-2)=42-2
40=40
also
3(12+3)=42+3
45=45

Hope this helps----ptaylor