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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
