Video Transcript
A man’s age is four times his son’s
age. In five years, the sum of their
ages will be 105, how old are they now?
So in this problem, we can see that
we could actually use two variables or one variable to solve it. Well, in fact, this is a good
example because we see it and think there’re two things there. But we can use only one variable if
we’d like to solve the problem. And this in fact makes the answer
simpler to come to. So what we done first of all is
we’ve selected a variable, and the variable is gonna be 𝑥. And what this is is the son’s
age. Could’ve been any letter, I just
decided to use 𝑥.
Okay, well, if the son’s age is 𝑥,
then the man’s age must be four 𝑥 because the man’s age is four times his son’s
age. And what these variables will
represent are the man and his son’s age now. But we’ve also been told that we’re
looking at their ages in five years’ time. So we could also then look at our
expressions for ages in five years’ time. First of all, the son’s age. Well, the son’s age is just gonna
be 𝑥 plus five. That’s because it’s in five years’
time, so we add on five. And therefore, the man’s age is
gonna be four 𝑥 plus five cause, again, we’re just adding five to his age now.
So now, to be able to form an
equation, we can use the other bit of information we’re given, and that is that the
sum of their ages in five years’ time is going to be 105. So therefore, we can form our
equation, which is 𝑥 plus five plus four 𝑥 plus five equals 105. So now, on the left-hand side of
the equation, what we can do is collect like terms. We’ve got 𝑥 add four 𝑥, which is
five 𝑥. And then we’ve got five add five,
which is 10. So therefore, we’ve got five 𝑥
plus 10 equals 105.
So now what we need to do is
subtract 10 from each side of the equation. So when we do that, we get five 𝑥
equals 95, and then we divide both sides of the equation by five, which will give us
𝑥 is equal to 19. So therefore, we can say that the
son is 19 years old. So now, what I want to do is find
out how old the man is now. Well, the man’s age is represented
by four 𝑥. So therefore, four 𝑥 is equal to
four multiplied by 19, as 𝑥 equals 19. So therefore, this would give us
76. So what we can say is that the son
and the man’s ages now are 19 years old and 76 years old, respectively.
