00:01
In this problem, we're told that a man is five times as old as his son.
00:05
And we're also told that two years ago, if we took the sum of the squares of their ages, we would get 1 ,114.
00:13
We want to define the present age of his son.
00:16
So let's start by defining our variables.
00:18
We want to define our variable s as the present age of the son, and f to be the present father age.
00:26
So what we know is that we need to set up a system of equations.
00:29
We know that if we take the son's age and we multiply it by five, we'll get the father's age.
00:38
And then if we go two years into the past and take two away from the son's age and square it, and take two away from the father's age and square it, and add those two together, we should get 1 ,114.
00:53
So we're going to make a substitution.
00:56
I'm going to replace f with 5.
00:59
5s.
01:00
So we have s minus 2 squared plus 5s minus 2 squared equals 1 ,114.
01:10
And remember that a plus b quantity squared is a squared plus 2av plus 2av.
01:19
And we get this 2ab by multiplying these together and doubling.
01:23
So i can quickly multiply this out.
01:26
We get s squared.
01:29
S is negative 2s, and we double it, we get negative 4s, and the negative 2 times negative 2 is 4.
01:35
And then 5s squared is 25s squared.
01:40
5s times negative 2 is negative 10s.
01:42
If we double it, we're going to get negative 20s, and the negative 2 times negative 2 is 4.
01:48
If you'd like, you can go through and foil that out, but that's the pattern that we're using here...