Welcome back.

I tried to start doing problem
number 10 in the last video,

but I realized I was running
out of time, so

let me start over.

Problem number 10.

The Smith Metals Company
old machine makes

300 bolts per hour.

Its new machine makes
450 bolts per hour.

If both machines begin running
at the same time, how many

minutes will it take the
two machines to make a

total of 900 bolts?

So the important thing
to realize is

that they said minutes.

So we could convert both of
these rates to minutes now, or

we could say how many hours is
it going to take, and then

convert that to minutes after
we have our answer.

Actually, let's do it the second
way, let's say how many

hours and then convert
that to minutes.

So let's say we want to
produce 900 bolts.

And how much are we going
to produce in each hour?

Well, they're both running
at the same time, right?

So in every hour, we're going to
produce 300 plus 450 bolts.

We're going to produce
750 bolts per hour.

Times, let's say x hours.

The units might confuse you, so
just leave out the units.

This is how many hours it takes
to produce 900 bolts, so

you divide both sides by 750.

You get x is equal to 900/750.

Let's see what I can do here.

See, if I divide the top and the
bottom by 30, the top will

become 30 over-- and then the
bottom, 75 divided by 3 is

20-- 75 divided by 3 is 25.

So 30/25.

Then I could-- let's see,
5 is a common factor.

I can do it all in
one fell swoop.

So that's 6/5.

So it's going to
take 6/5 hours.

That's how long it's
going to take us.

How many minutes is that?

Every hour is 1 minute--
I mean, sorry,

every hour is 60 minutes.

It's getting late.

So 6/5 hours.

You just have to multiply it by
60 to get how many minutes

is equal to-- see, you can
cancel this 5, make this a 12.

You get 6 times 12
is 72 minutes.

And that is choice B.

Next problem.

I've been using this yellow
a while, let me switch.

Problem 11.

The table above gives the values
of the linear function

g for selected values of t.

Which of the following
defines g?

OK, so they say t and
they say g of t.

They go from negative 1, 0,
1, 2, let's see, it's

4, 2, 0, minus 2.

So the one thing I always look
at is what g of 0 is because

that tends to be interesting.

Especially when I look at
all of the choices.

All of the choices are of this
form, they're all of the form

m times t plus B.

Where m is the slope-- if you're
familiar with linear

equations, you're familiar
with this form.

And so when t equals 0, g of t
tells you what the y-intercept

is going to be, right?

So let's see, g of
0 is equal to 2.

So that tells us that this
equation g of t is going to be

equal to the slope times
t plus 2, right?

Because when t was 0, all
we had left with was 2.

And so immediately, we can
cancel out all but the last

two choices.

So the last two choices, choice
D is g of t is equal to

minus t plus 2.

And then the last choice
is g of t is equal to

minus 2t plus 2.

Let's see which one of
these works, we can

try out some numbers.

So what happens when
t is negative 1?

When t is negative 1, this
expression becomes negative 1

times negative.

Negative negative 1 is positive
1, so this becomes 3.

That's not right.

This one becomes negative
2 times negative 1 is

positive 2, plus 2.

So this becomes 4.

So we can immediately cancel
this one out because it

didn't-- here, for this g of t,
g of negative 1 equaled 3,

and they tell us right here
it's supposed to equal 4.

This one worked.

And this is kind of the only
one that still works.

It had a 2 for the y-intercept,
and when you

evaluate it for just even
the first point, you

got the right answer.

So that's the answer,
the answer is E.

Next problem.

OK, survey results.

I guess I should draw this.

I haven't read the question, but
it's probably important.

Let's see, there's about
five squares that way.

So that means I have to draw
four lines, that's 1, 2, 3, 4.

And then eight lines
I have to draw.

1-- that's always the hardest
part, just drawing these

diagrams-- 2, 3, 4-- and you're
learning how to count--

5, 6, 7-- almost
there-- and 8.

All righty.

And then they say, these
are the grades--

the y-axis is grade.

Grade 9, 10, 11, 12.

The x-axis is distance
to school in miles.

1, 2, 3, 4, 5, 6, 7, 8.

And these are the points.

1 comma 10 is right here.

2 comma 9.

2 comma 11.

3 comma 10.

3 comma 12.

4 comma-- let's see,
4 is at 10 and 11.

5-- they have one point at 11.

6 has three points right
here, 10, 11, and 12.

Let's see.

There's a point here,
here, here.

And then a point
here and here.

Now we can start the problem.

The results of a survey of 16
students at Thompson High

School are given in
the grid above.

It shows the distance to the
nearest mile that students at

various grade levels
travel to school.

So this is miles.

And this is grade.

According to the grid, which
of the following is true?

So I'll just read them out.

A, there's only one student
who travels

two miles to school.

Let's see, two miles.

False, there's two students.

There is this guy
and this guy.

So it's not A.

Choice B, half of the students
travel less than

four miles to school.

So that's-- less than four miles
is everyone to the left

of this line, right?

And this is actually
1, 2, 3, 4, 5.

5 out of 16 is not half, so
we know it's not choice B.

C, more 12th graders than 11th
graders travel six miles or

more to school.

So they're saying more 12th
graders than 11th graders.

So six miles or more.

So let's see, six miles or more
is anything to the right

of this line, right?

That's six miles or more.

There are three 12th graders.

And how many 11th graders
are there?

There are two 11th graders.

I think that is correct.

More 12th graders than 11th
graders travel six or more

miles to school.

Six or more miles, three 12th
graders, two 11th graders.

That's our answer,
our answer is C.

Next problem.

I don't know if I'll have time
for this one, I'll try.

Problem 13.

How many positive three digit
integers have the hundreds

digit equal to 3 and the units
digit is equal to 4.

So it's going to be
like 3 blank 4.

So how many numbers are here?

Well, how many digits can
we stick in for that?

Well, we could put a
0, a 1, 2, 3, 4, 5,

6, 7, 8, or 9 there.

We could put any of those
in that middle spot.

And there are 10 digits we can
put there, so there are 10

possibilities.

There are 10 positive three
digit integers that have the

hundreds digit equal to 3 and
the units digit equal to 4.

That's choice A.

That's one of those problems
that you question yourself

because it seems maybe
even too easy.

I'll see you in the
next video.