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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 some discount problems
and these are the two problems
we do on this video.
We're going to work
with discount problems.
They're very similar
to market problems except
that we have a selling price
of something and we're going
to markdown.
There's going to be some sort
of discount.
So in discount problems it's
really a percent decrease type
of problem.
You're decreasing the price
and it's based
on what the selling price was
like, 10 percent off,
20 percent off.
And the terms we usually see
are discount rate
or markdown rate.
So when you see discount rate
or markdown rate,
we're referring to the percent
of the discount
on the original price.
Now the amount
of money an item is reduced
by is called the discount
or the markdown.
So it talks
about what's your discount it
means how much money did you
actually save?
So let's do this
discount problem.
A $425 dresser set is on sale
for 35 percent off the
regular price.
So we're assuming
that is the regular
price here.
Find the sale price.
Okay, there are a couple
of ways you can do this
but a common way is
to simply take the 35 percent
off of the regular price.
So that would be
your discount.
How much you're going
to take off.
So we would have
to do 35 percent of 425
to figure that out
which is .35 times 425.
Now in terms of money,
of course,
it's going to be dollars
and cents,
so you can either get a
calculator
out to figure this one
or you can do multiplication
on a piece of paper.
And this comes
out to this much money,
148.75, pretty good.
Now the one thing I'm going
to do before going on to see
if this seems
like a reasonable amount.
Thirty five percent is
about a third, okay, Right.
It's a little more
than a third.
So the question is the $148.75
is that about approximately a
third for $425?
And of course,
a lot of people have trouble
taking a third of $425,
but you could sort
of just estimate it, you know,
think of the 148.75
as about a $150, okay.
So if I multiple by three,
I should get the whole price.
That would be 450,
but it was really 425.
So it looks like it's
in the ballpark
so that's important.
See if it's in the ballpark.
So the discount $148.75; now,
what it's asking us
for is the sale price.
So how do you get the
sale price?
You have to subtract
that from the regular price.
So the sale price would be the
original price
of the dresser $425, right,
minus, I'm going to put it
in dollars and cents $148.75
and now you just do
that arithmetic.
You can do
that on your scratch paper
if you'd like.
I'm not going to take
up the space here.
That comes out to $276.25.
So that is the sale price
for that dresser.
So it's a pretty
good discount.
Right. Almost $150.00 off,
of course,
this is not a cheap set
obviously in the first place.
Okay, what's another way?
I said there was another way
of doing it?
If you want
to get the sale price,
you can think of it this way.
If you want
to get it directly.
If it's 35 percent off,
then you're still paying 65
percent of the original
dresser set price, right?
Because I got
that by subtracting 35
from 100 or saying 35 plus
what is 100?
So another way
to get the sale price,
a direct way, I often do this
so I don't have
to do two sets is I just want
to do 65 percent of the $425.
So I only have
to pay 65 percent
of that $425, right,
because I don't have
to pay the other 35 percent
because I get that's how
much off.
So now, that's .65 times $425
and same thing,
you either want to do
that multiplication or put it
into your calculator
which I'm doing right now
and speaking.
And I get on my calculator
$276.25, same answer.
So no matter how you do it,
you should get
that the sale price
is $276.25.
So here's our next problem.
A $310 bicycle is
on sale for $248.
What is the discount rate?
All right.
So we're looking
for the percent this time.
Right. And we need
to know what the markdown was
because remember the discount
rate is the same thing
as the percent decrease.
So the percent decrease
which is the same thing
as the discount rate, right,
another word for that,
that's the same thing
if the decrease amount,
how much it was decreased by,
right, over the
original amount.
And I'm not given
that decrease amount.
I know the original amount.
It was a $310 bicycle, right?
So I'm looking
for a percent here.
And I know the
original amount.
I need to find the decrease
of that.
In other words,
how much off was it
in terms of money?
All we need
to do is subtract 310
minus 248.
I think that's 62.
So it was decreased by $62.
Be careful
that you don't put 248
in the numerator.
Okay. And then we need
to change this to a percent.
So I can reduce first the
numerator by 100 percent,
I'm going to go ahead
and multiply
by 100 percent first.
All right, so if I multiply
by 100 percent,
now you can get
out a calculator and do this,
but it's actually pretty easy
to do without a calculator,
if I divide the top and bottom
by 10 and that takes away both
of the zeros,
and now I've got 62 divided
by 31.
Did you notice?
That's just 2 times
that 10 percent.
So that's what we're
looking for.
The discount rate is
20 percent.
So this was a 20 percent
off sale.
And now let's just check it.
Check. What is 20 percent
of 310?
Okay. So, what's 20 percent
of 310?
Well, its .2 times 310
which is 62
which is how much it was
decreased by, right?
We took the 310 minus the 62,
we get the 248.
And do you remember another
way to figure
out what 20 percent of 310 is?
You can say well,
10 percent off will just be
$31, so 20 percent off would
be twice that two times 31,
62.
So again, you sort
of can check it out.
Different ways of thinking
about it but in the end make
sure you go back use your
common sense and see
if that all make sense.
So this was a 20 percent
off sale.
That's what it was asking
and it says,
what is the discount rate?
Remember to write your answer
with a percent sign.
[Pause]
>> Please visit my website
at YourMathGal.com
where you can view all
of my videos by topic.