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>> Alright and these are expressions we are going
to define.
One object of quantity in terms
of another object, another quantity.
So instead of explaining it, let's just get to it.
If the length is four feet more than the width,
express the length and the width using one variable.
So we're only going to have one letter, and if you look,
we have length and we have width.
These two here.
So one of these will be X,
and one of them is going to be an expression.
Well if you read the problem, it's going to tell you
which one you're going to assign,
which is the best choice.
If the length, right here is the length is, is is equals, four,
more than means plus, width, width W. Right there,
we just defined the variable.
If you introduce a letter, it has to have some sort
of meaning, and in this case it was the width.
So the width is W, and now you can go back and look
at the translation, and it says the length is four plus W.
So we can say that one is four plus W.
And that's what we're going to be doing
in every single expression.
In every single problem on here.
One of these problems is going to get some expression
that involves the letter that we're introducing,
so let's look at number 2.
It says, this is a little more difficult,
but there are four times as many apples as pears in a bowl.
Express the number of apples and pears using one variable.
So what we have is number of apples and a number of pears.
And we want to think, well we're going to have four times one
of them, that's what it means.
Well does that mean, if you read it, four times as many apples
as pears, in a bowl, does
that mean we have more apples or pears?
More apples.
How many more?
Well, we have four times as many as the pears.
And that's what we get, four P and P. So if we had five pears,
we'd have four times as many apples as pears.
So if we had five pears, we'd have 20 apples.
And that's all you're doing on each of these.
One of them is going to be a letter, the other one's going
to be an expression based on that letter.
So let me get you started on the next one.
I've got a bunch of problems for you to try, and we'll go back
over all of them together, but I want you to try them first.
So. Starting the first one, it says the base
of a triangle is four feet less than the height.
Express the height and the base using one variable.
So we're going to call one of these the height,
and the other is going to be the base.
Now you have to decide which of these will get the variable,
and which will get the expression.
So I want you to try it.
Hit pause, and try it.
Once you finish number 3, un-pause it,
and the answer will appear.
[ Silence ]
>> Alright and then there's the answer.
So it says that the base of the triangle,
so we're giving the base the expression, is four less
than the height, which means the base of the triangle has
to be H minus four, and since we said the height is H,
we have to say the height is H. We're giving
that H a definition.
Alright, here's our next one.
Let's see if you can do it all by yourself.
So again, we're going to find
out how many different objects we have in here.
You're going to define one of them as a variable,
and the other one, or others,
has some expression based on that variable.
I only want to see one H or one S or whatever letter you choose
to use on this one, so hit pause, and give it a shot.
Alright, and here's sort of the answer.
I did this one, mistakenly, on purpose -
or incorrectly on purpose.
Can you figure out why?
It says the slower cyclist.
All that's doing is describing the person,
I could draw a picture of a slower cyclist.
It's not what we're looking for.
It says express the speed,
so this is the slower cyclist's speed,
and this is the faster cyclist's speed.
We really want to describe these correctly.
When you're talking about height and base, they already include,
I mean technically we're supposed to put the length
of the height and the length of the base,
but we can always say height, base, length and width
because that's what we're basically dealing with.
When we're talking about height, we're talking
about the actual height of an object, how tall it is.
So you don't have to put anything other than height.
But when you're talking about a person, they have speed.
They have other attributes.
So you need to actually describe them correctly.
The faster cyclist would be six plus X
and slower cyclist is X. Alright.
It'll - trust me, I know this seems very picky,
but when you start doing word problems this makes a
huge difference.
Alright, here's another one.
Give it a shot.
Hit pause.
And there's the answer.
So you should have number of moons of Saturn, seven plus J,
number of moons of Jupiter, J. Again,
if you put Jupiter equals J
and Saturn equals seven plus J, it's half correct.
It's not a good description.
It's just good placement of variables.
I'd rather see number of moons, number of moons.
Alright, let's try another.
Sale price of a suit.
Hit pause and try it.
And there's the answer, sale price is three-fourths
of the original price, so three-fourths times X,
and that means our X is the original price.
I didn't use O because it looks like a zero.
You don't want to pick letters that look like numbers.
Alright. Hit pause, try the next one.
Alright if you struggle with this one, that's great,
it's a very, very tricky one.
That's why it's the last one.
If you got it right, you're amazing,
it's an absolute amazement, because this is a difficult one.
But basically any time you're given a total number of coins,
one of them is going to be X, and it didn't matter
which one you assigned X, it could have been the number
of dimes, or the number of nickels.
But the other quantity, the other object had
to be twelve minus X because, that's what's left.
Think about it.
Let's put a different color here, we'll do red.
Let's just say the number of dimes, we had seven dimes.
How many nickels are there?
Well, there's twelve, take away seven,
it's always going to be that twelve.
So if you had five dimes, the number of nickels would be?
Twelve minus five.
So that's why we're putting twelve minus X. Whatever we
assign for the number of dimes, then the number
of nickels will be whatever is left,
which is twelve minus that number.
Alright. Thank you.