Posted by lele on Thursday, April 30, 2009 at 10:10pm.
Let f = father's age and s = son's age.
"the father's age is three times his son's age"
f = 3s
"the difference between a father's age and his son's age"
f - s
If we want to know f - s, and have f = 3s, then we need to subtract s from the left side. And what we do to one side of an equation we must to the other side as well, so we subtract s from both sides.
(f) - s = (3s) - s
f - s = 2s
Now try some numbers for the son's age.
If the son is 14 (s = 14), then the difference between the father's and son's age would be 2s = 2(14) = 28. Does that work? The father is 3x the age of the son, so if the son is 14, the father is 3 x 14 = 42. And yep, 42 - 14 = 28.
If the son is 17 (s = 17), then the difference between the father's and son's age would be 2s = 2(17) = 34. Does that work? The father is 3x the age of the son, so if the son is 17, the father is 3 x 17 = 51. And yep, 51 - 17 = 34.