SOLUTION: In five years time a father will be three times as old as his son. Five years ago, the father was six times as old as his son. Find their present age.

Question 120849: In five years time a father will be three times as old as his son. Five years ago, the father was six times as old as his son. Find their present age.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=son's present age; x+5=son's age in five year's time; x-5=son's age five year's ago
And let y=father's present age; y-5= father's age five years ago and y+5=father's age in five year's time
Now we are told that:
y+5=3(x+5) get rid of parens
y+5=3x+15 subtract 5 from both sides
y+5-5=3x+15-5 collect like terms
y=3x+10-----------------------------------------eq1
and that:
y-5=6(x-5) get rid of parens
y-5=6x-30 add 5 to both sides
y-5+5=6x-30+5 collect like terms
y=6x-25------------------------------eq2
Substitute y=3x+10 from eq1 into eq2:
3x+10=6x-25 subtract 3x from and add 25 to both sides
3x-3x+10+25=6x-3x-25+25 collect like terms
35=3x divide both sides by 3
x=11 2/3 years-----------------present age of son
substitute 11 2/3 for x into eq1:
y=3*(11 2/3)+10
y=35+10=45 years---------------------present age of father
CK
y+5=3(x+5)
45+5=3*(11 2/3)+15
50=50
and
y-5=6(x-5)
45-5=6*(11 2/3)-30
40=70-30
40=40
Hope this helps---ptaylor
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