Three years ago, a father was 4 times as old as his son. At present, the father is 3 times as old as the son. How old was the father three years ago?

Answer 1

Math isn't my greatest subject, but I'm hoping my explanation can make sense.

Let's not focus on the numbers right now, only the time. So in three years (from 3 years ago to now), the dad has gone from 4 times as old to 3 times as old. So let's consider how the dad changed from time one to time two: he gained 3 years. So to compare time one and time two, the dad's age now is 4 times the son's old age + 3. Now, the dad is three times the son's age from three years ago; to put this in terms now, we'll say the dad is 3 times (son's old age + 3). This is so we remember that the son and the dad's ages changed. Let's use s to represent the son's age from three years ago, since this will be the easier time to consider.

Let's say 4s + 3 = 3(s+3). [In other words, the dad's current age is three times his son's age from three years ago + three years which is also equal to three times the son's age from three years ago and 3.]

So now we can solve for s (the son's age from three years ago). Subtract 3 from both sides, then subtract 3s from both sides, and you're left with s = 6. In other words, three years ago, the son was 6 years old. So now we go back to the formula in the original problem. Three years ago, the dad was 4 times the son's age. So 4 times 6 = 24!

I hope that helped.