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Welcome back.

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

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but I realized I was running
out of time, so

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let me start over.

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Problem number 10.

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The Smith Metals Company
old machine makes

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300 bolts per hour.

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Its new machine makes
450 bolts per hour.

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

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minutes will it take the
two machines to make a

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total of 900 bolts?

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So the important thing
to realize is

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that they said minutes.

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

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

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convert that to minutes after
we have our answer.

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

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hours and then convert
that to minutes.

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

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

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

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

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We're going to produce
750 bolts per hour.

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Times, let's say x hours.

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

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

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you divide both sides by 750.

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You get x is equal to 900/750.

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Let's see what I can do here.

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

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

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20-- 75 divided by 3 is 25.

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So 30/25.

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

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I can do it all in
one fell swoop.

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So that's 6/5.

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

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

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How many minutes is that?

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

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every hour is 60 minutes.

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It's getting late.

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So 6/5 hours.

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

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

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You get 6 times 12
is 72 minutes.

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And that is choice B.

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Next problem.

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

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Problem 11.

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The table above gives the values
of the linear function

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g for selected values of t.

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Which of the following
defines g?

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

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

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4, 2, 0, minus 2.

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

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that tends to be interesting.

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Especially when I look at
all of the choices.

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

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m times t plus B.

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

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equations, you're familiar
with this form.

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

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is going to be, right?

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

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

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equal to the slope times
t plus 2, right?

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

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

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two choices.

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

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minus t plus 2.

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

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minus 2t plus 2.

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

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try out some numbers.

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So what happens when
t is negative 1?

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When t is negative 1, this
expression becomes negative 1

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times negative.

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

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That's not right.

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This one becomes negative
2 times negative 1 is

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positive 2, plus 2.

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So this becomes 4.

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So we can immediately cancel
this one out because it

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

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

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This one worked.

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

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

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evaluate it for just even
the first point, you

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got the right answer.

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

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Next problem.

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OK, survey results.

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I guess I should draw this.

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

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

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

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And then eight lines
I have to draw.

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

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

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

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All righty.

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And then they say, these
are the grades--

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the y-axis is grade.

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Grade 9, 10, 11, 12.

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The x-axis is distance
to school in miles.

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

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And these are the points.

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1 comma 10 is right here.

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2 comma 9.

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2 comma 11.

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3 comma 10.

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3 comma 12.

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

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5-- they have one point at 11.

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

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Let's see.

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There's a point here,
here, here.

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And then a point
here and here.

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Now we can start the problem.

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The results of a survey of 16
students at Thompson High

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School are given in
the grid above.

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It shows the distance to the
nearest mile that students at

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various grade levels
travel to school.

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So this is miles.

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And this is grade.

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

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So I'll just read them out.

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A, there's only one student
who travels

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two miles to school.

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Let's see, two miles.

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False, there's two students.

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There is this guy
and this guy.

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So it's not A.

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Choice B, half of the students
travel less than

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four miles to school.

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

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of this line, right?

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

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

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

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more to school.

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

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So six miles or more.

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

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of this line, right?

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That's six miles or more.

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There are three 12th graders.

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And how many 11th graders
are there?

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There are two 11th graders.

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I think that is correct.

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

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miles to school.

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

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That's our answer,
our answer is C.

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Next problem.

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

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Problem 13.

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How many positive three digit
integers have the hundreds

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

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

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So how many numbers are here?

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

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

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6, 7, 8, or 9 there.

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We could put any of those
in that middle spot.

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

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possibilities.

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There are 10 positive three
digit integers that have the

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

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That's choice A.

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That's one of those problems
that you question yourself

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because it seems maybe
even too easy.

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I'll see you in the
next video.