Video Transcript
I am thinking of two numbers. Use the clues to determine what the
numbers are. When you divide one by the other,
the quotient is eight. The sum of the two numbers is
81.
So in this problem, what we have
are two variables because we’re told that we need to find two numbers. So therefore, what we’re gonna call
these variables is 𝑥 and 𝑦. So now what we can do is set up a
couple equations using our two clues. We’ll use the first clue. We’re told that if we divide one by
the other, the quotient is eight. So therefore, we can set up our
first equation which is 𝑥 divided by 𝑦 is equal to eight. And that’s because the quotient is
the result of a division. And I’m gonna label this equation
one cause this helps us as we go through our method.
Now, we can take a look at the
second clue and set up an equation using this because we’re told that the sum of the
two numbers is 81. So therefore, we have 𝑥 plus 𝑦
equals 81. And we’ve called this equation
two. So now, what we’ve got is a pair of
simultaneous equations. So what we’re gonna use to solve
these simultaneous equations is a method called substitution. And to do this, we need to
rearrange one of our equations so that 𝑥 or 𝑦 is the subject. Well, in fact, you could use either
of the equations, but what we’re gonna use is equation one. And we could rearrange this by
multiplying each side of the equation by eight. And when we do this, we’ve got 𝑥
as a subject to the equation cause 𝑥 is equal to eight 𝑦. And we’re gonna call this one
equation three.
So as we said, we’re gonna be using
the substitution method. So what we can do now as we’ve got
𝑥 as the subject is substitute equation three into equation two. As I said, we could’ve made 𝑥 or
𝑦 the subject and we could’ve rearranged either equation one or equation two. It’s just that we chose to do
equation one. So now that we’ve substituted in
equation three into equation two, we get eight 𝑦 plus 𝑦 equals 81, which is gonna
give us nine 𝑦 is equal to 81. So then, we divide each side of the
equation by nine and we get 𝑦 is equal to nine. So great! What we’ve done is we’ve found our
first variable or, in fact, our first one of our two numbers.
So now to enable us to find our
other variable 𝑥, what we’re gonna do is we substitute 𝑦 equals nine into one of
our other equations. Well, in fact, the best one to
substitute it into is equation three because we already got 𝑥 as the subject. And when we do this, what we get is
𝑥 is equal to eight multiplied by nine. So this’s gonna give us 𝑥 is equal
to 72. So therefore, we can say that our
values are gonna be 72 and nine.
And what we can do is we can
double-check this by substituting them back into our original equations that we got
from our clues. So if we look at our first clue or
our first equation, we’re gonna have 72 divided by nine is equal to eight. Well, yes, this is correct because
72 divided by nine is eight. Well then for our second equation,
we got 𝑥 plus 𝑦 equals 81. Well, we’ve got 72 plus nine equals
81. So again, this is correct. So therefore, yes, 72 and nine are
our two numbers.
