Question 120849

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