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.