Carton Quantity Video Lecture - Sales

- [Voiceover] Sarah bought a
total of 20 cartons of paper.
If she paid $50 per carton
for some of the paper,
and $30 per carton for the rest,
and if the total bill was $900,
how many of the $50 cartons did she buy?
So let's define some variables here.
Let's let x equal the
number of $50 cartons
and let's let y equal the
number of $30 cartons.
If we just take the number of cartons,
so the number of $50 cartons
plus the number of $30 cartons
we know that's going to be
the total number of cartons.
And they tell us what that is,
they tell us that she bought a
total of 20 cartons of paper.
So x plus y is going to be 20.
Now let's think about how much
did she spend on $50 cartons?
Well she bought x cartons and
then each of them were $50.
So it's going to be 50 times x.
If she bought two cartons
it would be 50 times two.
If she bought three cartons,
it would be 50 times three.
So if this is how much
she spent on $50 cartons,
how much did she spend on $30 cartons?
Well it's going to be the
number of $30 cartons times $30.
If she bought one, it would be $30.
If she bought two, it would be $60.
So this is the total amount
she spent on $50 cartons,
total amount she spent on $30 cartons,
and then if you add these together
you're gonna have your total bill.
And they tell us that
the total bill was $900.
So this is going to be equal to $900.
Now what do we need to solve for?
How many of the $50 cartons did she buy?
So we really just wanna solve for x,
the number of $50 cartons.
So the easiest way to solve for x
is to try to eliminate this y here.
And the easiest way to eliminate this y
is if I could turn this into a minus 30 y
and then add the two
equations to each other,
add the left-hand side
and the right-hand side,
then the y's would cancel out.
You could also do this
through substitution,
there's a bunch of ways you could do that.
But let's try to turn
this into a negative 30 y.
The easiest way to do that
is to multiply both sides of
this equation by negative 30.
So you have negative 30
times x minus 30 times y.
I just took the negative thirty
multiplied it times each of these,
is equal to negative 30,
so if we multiply that times negative 30,
20 times negative 30 is going to be what?
It's going to be negative 600.
And now we can add the left-hand
side to the left-hand side
and the right-hand side
to the right-hand side.
On the left-hand side, 50 x minus 30 x,
that's going to give us 20 x.
And these cancel out,
that was the whole point.
And on the right-hand
side, 900 minus 600 is 300.
And so, let me just write over here,
we have 20 x is equal to 300.
Now to solve for x we just
divide both sides by 20.
So let's just divide both sides by 20.
We are left with x is
equal to 30 over two,
or x is equal to 15.
She bought 15 $50 cartons.