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>> Hi. This is Julie Harland
and I'm your math Gal.
Please visit my website
at YourMathGal.com
where you can search for any
of my videos organized
by topic.
We're going
to do a couple more
markup problems.
These are a little bit more
involved than what we've done
so far, so these are the two
problems we're going to do
on this video.
All right,
let's try this markup problem.
A retailer uses a markup rate
of 24 percent.
The markup
on an item was $76.80.
Find the cost of the item
and the selling price
of the item.
Now keep in mind,
the markup means the profit.
That's how much they add
to the original cost
of the item.
So whatever the original cost
was they ended
up taking 24 percent of that
and that must have been
the $76.80.
And then they added it
to that cost
to get the new selling price.
So we have to sort of think
about what we know here.
We know that 24 percent is
what they used of the cost
of the item
and we don't know the cost.
So we need to start off
with letting
that be our variable.
Let's let this be the cost
of the item.
So we know that 24 percent
of that cost is how much
they're going to mark it up,
that's what that 76.80.
That's not what they sell it
for, right?
That isn't the cost
of the item
and that's not what they sell
it for.
That's how much they're adding
to the cost of the item.
So, I know that 24 percent
of the cost is that $76.80.
So that's what we want
to write as an equation.
How do you write 24 percent?
Well, that's .24 and the cost,
you're going to multiply
that by the cost,
that's just C.
So we have point 24C.
That is the same thing
the 76.80.
Okay, now that's going
to give us the cost
which is part of this problem.
So we're just going
to divide both sides by .24
and what does that give?
So you get
out your calculator unless you
want to go ahead
and do your long
division here.
And I came up with 320.
So that must be the cost
of the item.
Now the question is what's the
selling price?
Well, you add what you marked
it up, right.
You marked it up $76.80.
So you have
to take the original cost,
add how much you marked it up,
and that should give us our
answer of the selling price.
All right.
So when all said and done,
what's the answer here?
It says find the cost
of the item
and the selling price
of the item.
So we could write the cost was
$320 and it sells for $396.80
and there we go.
Now does that seem reasonable
to you?
You buy something for $320.
You mark it
up about 25 percent.
That's about a quarter?
Right. So let's think
about that, 320,
what's a fourth of that?
That's 80 bucks right?
Eighty bucks,
well if you added 80 bucks
you'd have $400.
Well, this is close
to $400 right,
because it's only 24 percent.
So that's going back
and making sure your answer
seems reasonable.
Okay. Let's try this
markup problem.
A jeweler uses a markup rate
of 150 percent.
You know what;
I think that's maybe
in the ballpark.
Sometimes it feels
like a 1000 percent.
But anyway, notice it's
over 100 percent.
That can happen to a person.
You don't have to mark it
up between zero
and 100 percent.
So if the jeweler sells a ring
for $2,100 how much profit did
the jeweler make?
Okay. So we know the selling
price and we know the markup
rate, right?
But we don't know the cost,
so we're going to have
to figure out the cost
in order to figure
out what the profit is.
And remember the profit is the
same thing as the mark up.
Well, lots
of words I'm throwing
out here.
All right,
so how do we want to start?
We know that the profit is
going to be 150 percent
of the cost
but we don't know the profit
and we don't know the cost.
So let's start off
by using a variable
for our cost.
So how about letting C be
the cost?
Don't make that common mistake
of trying to take 150 percent
of $2,100.
It's 150 percent of the cost
of the jewelry.
That's how they decide how
much to add
and get their selling price.
Okay. So if C is the cost,
what happens?
The jeweler buys it.
That's what it costs
and then they're going
to mark it up.
Now how much are they going
to mark it up?
They're going to mark it
up 150 percent.
Now how do you write
150 percent?
Well, divide by 2
or move the decimal two
to the left, that's going
to give you 1.5.
So you're going to have 1.5C,
150 percent of the cost
of that jewelry.
So we've got the original cost
plus we're going
to mark it up.
Here's your markup right here
and that's what they're going
to sell it for, $2100.
So now we have to remember how
to add like terms over here.
Remember, even though you
don't see it,
there's a hidden coefficient
of 1, so that we can add
like terms here.
So what's 1 plus 1.5?
It's 2.5. Now we'll just
divide both sides by 2.5.
Obviously,
you can use a calculator
but you can get out a piece
of paper and do
that long division as well.
So what is 2100 divided
by 2.5?
I got 840.
So it looks
like the original cost
was 840.
Now is that what we're
being asked?
It says how much profit did
the jeweler make?
Uh, ha, that's a
different question.
How do you get your profit?
There's two ways
of thinking of that.
What's the markup,
which you could get
by doing 150 percent of 840,
or just subtract?
Take how much you sold it for,
so here's the profit here.
You're going
to take what you sold it
for 2100 and subtract 840.
So let's see, you're going
to do that arithmetic
and that's going
to give you $1,260 in profit.
Okay. So that's what the
profit is.
Now let's just do a
double check.
Let's check,
what is 150 percent times 840?
Let do it a simple way.
Well, it's a 100 percent,
so at least the 840 plus 50
percent more.
All right, so 840,
what's half of 840?
That's 420 more, that is 1260,
so that's a check as well,
that your markup, right,
150 percent of 840
or you could check it
by just actually doing 150
percent which is 1.5 times
840, which yes,
that's 1260 as well.
So I'm checking it more
than one way.
You want to see
if it all makes sense.
If that profit,
does that make sense?
Is that the real markup 1260
bucks and yep,
that's the markup.
That's how much the
jeweler's making.
Yes, that's common
in jewelry store.
So the question is how much
profit did the jeweler make?
And all we have
to do is answer the question.
The jeweler made $1260 profit.
So a lot of this is common
sense and reasoning
through what you know,
what you have to figure
out first, how could you sort
of check it,
and make sure it all
makes sense.
[Pause]
Please visit my website
at YourMathGal.com
where you can view all
of my videos
which are organized by topic.