Tip:
Highlight text to annotate it
X
>> All right, these are percent decrease problems.
There a application that we were doing before
which is a percent word problems.
These are more of a life situation
that we're going to run into.
So let's just try them.
A shirt you have been looking at is 20 percent off.
If the regular price is 45 dollars,
then what is the discount for the shirt?
So, it's a percent problem 'cause we have a percentage
in there.
So what we have to do is write our part, our base,
and our reference percent again just like before.
So since we're given the percentage,
let's put that in there first.
It's 20 percent off, which means the part represents the amount
that we get off.
All right, regular price will always be the base 'cause you're
always going to take that regular price and you're going
to take a percentage off of it.
It is our-- the percent that we're-- it's the part.
It's what we're going to take the percent off of,
which means we are looking for this right here.
And it also says what is the discount.
And the discount is the amount we take off.
So if we put 20 percent here, we put X here,
and 45 here 'cause that's the 100 percent, that's 45.
This is our regular price, it's 100 percent.
This is our discount, and that's the 20 percent.
And then we cross multiply.
So 100 X, 45 times 20 divided by 100, and X equals--
[ Pause ]
-- 9. And again, if you want to figure out what
that is, it's 9 dollars off.
It's our discount.
So that is our discount, 9 dollars.
OK, part two, this is where the percent decrease comes
in to part.
So, with the discount, it's actually going
to be decreasing the price.
Our regular price was 45 dollars.
We're going to have a discount of 9 which gives us a sale price
of 36, and that's a decrease.
So that percentage actually represents a decrease
in our regular price.
That's why we call them percent decreases.
So that's all it is.
It's the percent that's actually going to be used
and removed from the base.
So, let's have you try one.
You have a 40 percent off coupon for the entire purchase.
If the regular prices for your items are 4 dollars, 5 dollars,
and 7 dollars, then what is your discount?
And then go on to B and find the sale price.
So hit Pause and give them a shot.
If you need a hint, first thing you want to do is add all
of these up and that will give you your base.
Hit Pause now.
And OK, and here is the answer.
So, you should've said 16 dollars,
that's the entire total of the regular price.
We're going to take 40 percent off.
So when we plug in our equation, that X is going
to give us the amount off.
We solve it and we get 6 dollars and 40 cents off right here.
So that is our discount.
So we take the 16 dollars, subtract the 6.40
and you get 9.60 for the sale price, all right.
Let's try to the percent discount.
This is a little bit different.
It's not a money situation.
Light beer has 20 percent fewer calories than the regular beer.
If regular beer has 180 calories,
then how many calories are in light beer?
OK. So the regular beer is our part--
I mean, our base because it's 20 percent fewer calories
than a regular beer.
So you notice we're using the word fewer,
which means after we get this number,
we're going to subtract it.
This is a percent decrease.
So we know it's 20 percent fewer, which means the amount
that we get is going to be the amount
that we get that is fewer, OK.
So we plug it in and that is 20 percent.
That's X and that's 180.
And we cross multiply.
[ Pause ]
Plug in the calculator.
[ Pause ]
And 36.
[ Pause ]
And it's fewer because that's what our percent represents.
So that's what the X represents.
All right, let's see if we answer the question now.
It says if regular beer has 180 calories,
then how many calories are in light beer?
Well, this gives us fewer calories, 36 fewer.
So that means we still have to do our actual decrease
which means to subtract.
So 180 minus 36 is 144 calories.
So how many calories are in light beer?
144. So that 20 percent off just basically tells us how much
to remove.
And when you see the word fewer, that's what you have to do.
But, the main thing with these problems is to always just put
that percent and then write the word
that that percent represents and put
that the same word on the part.
That way we know exactly what our answer is.
It tells us the amount that is fewer.
All right, let's try one more.
In one year your car decreases 4,000 dollars.
If your car is worth 45,000 dollars,
then what is the percent decrease for one year?
So in this one they're asking for the percent decrease,
which mean somewhere in this problem there has to be
that the same word and there it is.
This decrease refers to our part because the part--
the percent is referring to.
It's referring to a decrease so that has to be there.
The car is worth 45,000, so that is the amount
that we're going to decrease.
That's our base.
And we are looking for the percent decrease.
That goes here, the 4,000 goes here, and our 45,000 goes there
because the 100 percent represents the car's
original value.
This is our decrease.
Both of them represent the decrease.
OK. So we get 4,000 times 100 equals 45,000X divided
by 45,000.
[ Pause ]
Oops, it went too many.
And there it is, 8.0--
if you want to see that again, 8 and a lot of 8s.
8.0-- we'll just say 8.9 percent decrease.
And how do I know to put the word decrease?
Because it's right there.
Decrease, decrease it tells us.
All right, let's try one more.
And then I'll give you one to try.
Oh, actually I-- OK, I have three there for you to try.
So that kind of space off but, OK.
Shoes that normally sell for 50 dollars are
on sale for 20 dollars.
What is the percent decrease?
So again, decrease.
So, shoes that normally sell for 50.
This is our original price.
So that has to be the base, OK?
What is the percent decrease?
We're looking for this.
So then-- oh, that just has to be the decrease, right?
Is it? No, it's the sale price.
Sale price doesn't represent decrease,
it represents what you pay after the decrease.
So how do you find the decrease?
We find out how much it was decreased.
50 minus 20 would give us a 30-dollar decrease,
a 30-dollar discount.
That's why the whole point was to put the word there
to make sure it actually matches.
So 30 goes here because that's our part, and X, and 50.
So we get 50X equals 30 times 100,
divided by 50, and X equals--
[ Pause ]
-- 60. A 60 percent decrease.
I like to put the word.
And there you go, it's a 60 percent decrease.
How can you check it?
Well, if you take 60 percent of 50
and we've already done mental math, right?
So what's 5 times 6?
30 dollars.
50 minus 30 would give us?
20. So it checks out.
All right, here's three more problems for you to try,
number six, number seven, and then number eight.
And these are all can be very, very quick tricky.
So, give them a shot.
In fact, why don't we just do six?
We'll do it one at a time.
So try number six and then we'll move
on together to the final two.
If you can do six, you should be good.
Hit Pause now.
OK, and you should've got a 23 percent discount.
So, the 40 dollars represents the sale price,
but it's not what we're looking for.
We're looking for the discounted rate.
By the way the word rate can also be used
to represent our percentage.
Discounted rate which means we need the discount.
They must match, right?
If we want a discounted rate, we want the discount.
So, 52 minus 40 is 12, that's where this comes from.
[ Pause ]
OK. So the next two can be a little bit tricky
but they're very important
because they make you really pay attention to the wording.
So, a shirt is on sale with a discount of 20 percent.
If the sale price is 35.95, then what is the original price?
So if you remember original price, this is our base.
So we're looking for the original price, all right.
And we have a discount of 20 percent.
So if you put 20 percent here with the discount,
then up here it must be the discount.
Well, we can't have two unknowns.
We're given a sale price not that the discount.
When this happens, what it means is the percent
that they're giving us is not the one that we're going to use.
What it is, is something that we're going to have to use
to find the actual percent.
So what we were given the only value is the 35.95 sale price,
which means the percent has to b--
the referring percent has to be the sale price.
So if you have-- think about it this way.
This is the original price.
And what we're going to do is come in here
and remove 20 percent.
Just full on take out 20 percent.
How much is left?
Oops.
[ Pause ]
How much is left?
80 percent.
This is what represents the sale price.
And we did this earlier when we did pie charts.
Or I can't just find it.
There we go.
There's our pie charts.
Right here, you see the discount?
If you have a discount of 10 percent and you remove it,
you're going to be left with 90 percent 'cause it's 100 percent
the entire thing, all right?
So, that means this sale price represents 80 percent.
So if you know the discount of 20,
you know what the sale percentage is,
you know that it has to be 80.
If you take off 25 percent that means you're going
to have to pay 75 percent.
So that means, we can put 80 percent here
and then we can put its matching 35.95 here.
Remember these have to match and they're both sale prices.
And we put the X there because that is the original,
that's the 100.
So we get 80X equals 35.95 times 100, divided by 80.
And what is that gives us on our calculator?
35.95 times 100 divided by 80, 44.94.
And there it is.
That is our original price, 44.94.
How can you figure out if you have it correct?
Well, just do the math.
If we do 44-- so a little checking here.
It's quiche there.
44.94 times 20 percent is what?
So 44.94-- 44.94 times 0.2 gives us 8.99, right?
OK. Now if we subtract it, 44.94 minus 8.99,
it gives us 35.95 that on sale price.
There it is.
[ Pause ]
Always check, we know how to find discounts fairly quickly.
So check it at the very end to make sure it works, and it does.
All right, last one.
This one is a trickier one.
Gala apples are on sale today for 1.30 dollar per pound.
This is a discount of 30 percent.
So what was the cost before sale?
So I want you hit Pause and try it.
Just try it.
If you get it wrong, you're going to be able
to correct it but try it.
Don't just wait for the answer.
Hit Pause now.
All right, so, 1.30 represents the sale price,
which means we need the percentage
that represents the sale price.
So if we take the 100 and minus 30, you get 70.
And that's what we have to use.
Do a little cross multiplying and you get 1.86,
and that's the percent decrease.
All we have left now is percent increase
and so that's the next video.