SAT Prep: Test 4 Section 4 Part 3

Welcome back.

We're on problem
number twelve.

The perimeter of a rectangular
plot of land is 250 meters.

If the length of one side of the
plot is 40 meters, what is

the area of the plot
in square meters?

So let me draw a
rectangle here.

We know that one side of
the plot is 40 meters.

Well it's a rectangle.

So if this side is 40,
then this side is

also going to be 40.

And let's say we don't
know the other side.

Well if this side is
x, this is also x.

So what is the perimeter,
expressed in these terms?

What's 40 plus 40, which
is 80, plus x plus x.

So if 80 plus 2x is the
perimeter, and we know that

the perimeter is 250.

And so solving for x we get 2x
is equal to, what's 250 minus

80, that's 170.

At that x is equal to 85.

And now if we want to get the
area of this, we just multiply

the base times the height.

So 85 times 40, put a 0 here,
and 4 times 5 is 20.

4 times 8 is 32, plus 2 is 34.

So the area is 3400
square meters.

I hope I didn't do something
wrong with the math, but I

think you get the point.

Next problem.

Problem thirteen.

A school ordered $600 worth
of light bulbs.

Some of the light bulbs cost $1
each, and others cost $2.

So some were $1, some
were $2 each.

If twice as many $1 bulbs as
$2 bulbs were ordered, how

many light bulbs were ordered
all together?

Fascinating.

So let's let x equal
number of $1 bulbs.

I could introduce a variable y,
but I could just say that x

is the number of $1 bulbs, and
we know that twice as many $1

bulbs as $2 bulbs
were ordered.

So how can I express the
number of $2 bulbs?

Well we know that twice
as many $1 bulbs were

ordered as $2 bulbs.

So this would be
x divided by 2.

There are half as many
$2 bulbs as $1 bulbs.

And we know that if we add up
the total number of bulbs,

well actually we don't know.

So what is the total cost if we
get x $1 bulbs, and if we

get x divided by 2 $2 bulbs?

What is going to be the
total cost of this?

Well, I'm going to get x $1
bulbs, and they're each going

to cost $1.

Plus, I'm going to get x over
2 $2 bulbs, and they're each

going to cost $2.

And when I add it all up it's
going to equal $600.

So x times 1 is, of course, x.

And then x over 2 times 2,
that's lucky that worked out,

plus x is equal to $600.

So 2x is equal to 600.

x is equal to 300.

And they want to know
how many lightbulbs

were ordered all together.

So we got 300 $1 bulbs, and we
got 1/2 as many $2 bulbs, x

divided by 2.

So we got 150 $2 bulbs.

So together we got 450 bulbs.

Next problem.

Image clear.

I'll do it in a new color
so we don't get bored.

Fourteen.

If 4 times x plus y times x
minus y is equal to 40, and we

also know that x minus y is
equal to 20, what is the value

of x plus y?

Well, we know x minus y is equal
to 20, so we can just

substitute that right here.

So then we get 4 times x plus y
times, instead of writing x

minus y we can just write times
20, is equal to 40.

Or, if we multiply 20 times 4,
we know that 80 times x plus y

is equal to 40.

Then we know, divide both sides
by 80, and we get x plus

y is 40 over 80.

Which is the same
thing as 1/2.

And that's our answer.

x plus y is equal to 1/2.

Next problem.

Fifteen.

In a rectangular coordinate
system, that's what we're

familiar with, the center of a
circle has coordinates 5, 12.

So I draw a circle, and then the
center of the circle has

the coordinates 5, 12.

And the circle touches the
x-axis at one point only.

What is the radius
of the circle?

So it just touches the x-axis.

And the only place where it can
touch the x-axis only in

one point is this exact.

Because the x-axis is
essentially a horizontal line.

And where else can you
touch the x-axis?

You could touch it
here, on top.

But if the x-axis was up here,
then the y coordinate would

not be positive.

So this has a positive y
coordinate, so we know it has

to be above the x-axis,
it's at 12.

So we know the only place where
you can touch the x-axis

just once is right here, just
right at the bottom.

So it's gotta be like that.

That's gotta be the x-axis.

That could be the x-axis and
then the y-axis could be out

here someplace.

Just so you have a frame
of reference.

And if that's the x-axis,
then what's the radius?

Well, this is the point 5,
12, this is y equals 12.

So what is this height?

This is a radius.

Well that's just the
y-coordinate, it's 12.

So the radius is equal to 12.

They're just saying what is
the radius of the circle,

well, the radius is 12.

It's the y-coordinate.

Next problem.

Whoops.

I say whoops a lot.

Problem sixteen.

They have this men, women,
woman, and then they say

voting age population.

So population, and then
registered, and they say 1200,

1000, 1300, and 1200.

They say, the table above gives
the voter registration

data for the town of
Bridgeton at the

time of a recent election.

In the election, 40%
of the voting age

population actually voted.

So this is the voting
age population.

And we know that 40%
actually voted.

If the turnout for the election
is defined by the

number who actually voted,
divided by registered, what

was the turnout for
this election?

So what's the number
who actually voted?

It's 40% of the voting
age population.

So what's the voting
age population?

Well the total population
is the men and

women, so that's 2500.

Just add these two up.

And what's 40% of 2500?

That's 2500 times 0.4.

Let's see.

4 times 25 is 100.

Two more zeros.

0, 0.

And then, of course,
one decimal.

So it's 1000.

I just took 40% of 2500.

1000 people voted.

And if we want to know the
turnout, we just have to say

the number voted, which is
1000, divided by the

registered voters.

Well the registered voters,
there's 1000 men, 1200 women,

so you add that up.

That's 2200 total registered
voters.

That's the same thing
as 10/22, or 5/11.

That's our answer.

That's the fraction
that voted.

That's what they wanted.

To find to be the fraction, so
you can write it as this

fraction, 5/11.

I'll see you in the next video,
hopefully I didn't make

them mad there.

See you in the next video.