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.