### Video Transcript

πππ is a straight line, where
the length ππ is seven times the length ππ. Given that ππ equals 120
centimeters, calculate the length of ππ.

Well, the first thing we can do is
actually start to form some equations using the information that we have. So we know that ππ is seven times
the length ππ. So we can rewrite this as ππ
equals seven ππ. And what Iβm gonna do is actually
label this equation one. So thatβs our first equation.

And next, what we can do is we can
say that ππ is equal to ππ plus ππ and thatβs because we know that πππ is a
straight line and π is a point on that straight line. So what Iβm gonna do is call that
equation equation two.

Okay, so now, whatβs my next
step? So the first thing we can do is
actually substitute equation one into equation two. And we can do that because we know
that ππ is equal to seven ππ and ππ also appears in equation two. And what weβre actually doing here
is solving a pair of simultaneous equations using substitution.

So therefore, when we do that, we
get ππ is equal to ππ plus seven ππ. And we got that because actually we
substituted in seven ππ for our ππ. And then when we simplify this, we
get ππ is equal to eight ππ. And thatβs because if we have one
ππ and we have seven ππs and add them together, we will get eight ππ.

So thatβs great because we now have
π in terms of ππ. So what we do now is actually
substitute in the fact that we know that ππ is equal to 120. And we get that from the second
part of the question. So when we do that, we get 120 is
equal to eight ππ.

Okay, now, what we can do is
actually solve this to find ππ. So to do that, what weβre gonna do
is actually divide each side of the equation by eight. And thatβs because we have eight
ππ and we want single ππ. So if you divide eight ππ by
eight, we get just ππ, which is what weβre looking for. But remembering that whatever we do
to one side of the equation, we got to do to the other side of the equation. And when we do that, we get 15 is
equal to ππ. So we now know that ππ is equal
to 15 centimeters.

Okay, great, so what do we need to
do next? Well, next, we need to look at the
question and see well what is it looking for. The question wants us to calculate
the length of ππ. So in order to actually find out
what ππ is and calculate that, what weβre gonna do is actually substitute our
value of ππ β so ππ equals 15 β into equation one. And when we do that, weβre gonna
get ππ is equal to seven multiplied by 15, which will give us a value of ππ of
105.

So therefore, we can say that if
πππ is a straight line, where the length ππ is seven times the length ππ, and
given that ππ is equal to 120 centimeters, the length ππ is 105 centimeters. So weβve got the answer, great! But what I wanna do here is just a
couple of things, just a sort of check.

First of all, Iβm just gonna show
you how we could actually check if that is the correct answer and then give you an
idea of another sort of visual method you could have used. So what weβre gonna do first is
actually look at a little check. And to do that, weβre gonna
substitute ππ and ππ into equation two.

So basically, what we know is that
ππ plus ππ should be equal to 120. So what weβre gonna do, weβll put
our values in. So weβve got obviously 105
ππ. And we found that ππ is 15. So we can see that actually yup,
when we add 15 and 105, we will get 120. So weβve checked it. So it works and thatβs equal to our
ππ value.

Okay and the last thing I wanted to
do is actually show you how we could have thought about this question, maybe with
more visual method. Well, if we think that we know that
ππ is seven times the length ππ, then we could have thought of our line, broken
down into these sections. So we have one which is between π
and π and then seven between π and π. So therefore, we would have had one
plus seven, which is eight parts. So we know that actually the full
line ππ would have eight parts.

So therefore, if we wanted to find
one part, weβd do 120, total length, divided by eight, which is given as 15. So we know that one part will be
worth 15. So therefore, if we wanted to find
ππ, well, we know ππ is gonna be equal to seven parts. So we do seven multiplied by 15
because 15 was the value for one part, which gives us 105, which is the same value
we got using the first method. So this is just another method you
could use if you preferred kinda of visual representation.