Question 949818
f = father's present age
s = son's present age
:
Write an equation for each statement
:
A father is three times as old as his son was n years ago.
f = 3(s - n)
f = 3s - 3n
f + 3n = 3s
 At that same time (n years ago), the father was twice as old as his son will be two years from now.
f - n = 2(s + 2)
f - n = 2s + 4
multiply this by 3, add to the 1st equation
3f - 3n = 6s + 12
f + 3n = 3s
----------------adding in eliminates n
4f = 9s + 12
:
 Find the present age of each is they sum to 55.
 f + s = 55
f = (55-s)
:
Replace f with (55-s) in the 4f = 9s + 12 equation
4(55-s) = 9s + 12
220 - 4s = 9s + 12
220 -12 = 9s + 4s
208 = 13s 
s = 208/13
s = 16 is the son's age
then
55 - 16 = 39 is father's age
:
;
Check this out, find n
f = 3(s - n)
39 = 3(16-n)
39 = 48 - 3n
3n = 48 - 39
n = 9/3
n = 3
"At that same time (n years ago), the father was twice as old as his son will be two years from now."
39 - 3 = 2(18)
36 = 36 confirms our solutions