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Welcome back.

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We're on problem[br]number twelve.

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The perimeter of a rectangular[br]plot of land is 250 meters.

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

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the area of the plot[br]in square meters?

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So let me draw a[br]rectangle here.

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

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Well it's a rectangle.

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So if this side is 40,[br]then this side is

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also going to be 40.

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

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Well if this side is[br]x, this is also x.

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So what is the perimeter,[br]expressed in these terms?

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What's 40 plus 40, which[br]is 80, plus x plus x.

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

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the perimeter is 250.

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

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80, that's 170.

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At that x is equal to 85.

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

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the base times the height.

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

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4 times 8 is 32, plus 2 is 34.

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So the area is 3400[br]square meters.

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

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think you get the point.

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Next problem.

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Problem thirteen.

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A school ordered $600 worth[br]of light bulbs.

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

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So some were $1, some[br]were $2 each.

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

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many light bulbs were ordered[br]all together?

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Fascinating.

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

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

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

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bulbs as $2 bulbs[br]were ordered.

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

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Well we know that twice[br]as many $1 bulbs were

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ordered as $2 bulbs.

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So this would be[br]x divided by 2.

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There are half as many[br]$2 bulbs as $1 bulbs.

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

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well actually we don't know.

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

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get x divided by 2 $2 bulbs?

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What is going to be the[br]total cost of this?

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

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to cost $1.

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

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going to cost $2.

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

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So x times 1 is, of course, x.

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

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plus x is equal to $600.

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So 2x is equal to 600.

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x is equal to 300.

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And they want to know[br]how many lightbulbs

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were ordered all together.

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

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divided by 2.

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So we got 150 $2 bulbs.

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So together we got 450 bulbs.

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Next problem.

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Image clear.

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

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Fourteen.

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

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

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of x plus y?

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

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substitute that right here.

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

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

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

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is equal to 40.

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

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y is 40 over 80.

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Which is the same[br]thing as 1/2.

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And that's our answer.

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x plus y is equal to 1/2.

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Next problem.

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Fifteen.

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

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

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

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the coordinates 5, 12.

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

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What is the radius[br]of the circle?

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So it just touches the x-axis.

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

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one point is this exact.

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Because the x-axis is[br]essentially a horizontal line.

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And where else can you[br]touch the x-axis?

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You could touch it[br]here, on top.

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

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not be positive.

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

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

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

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just once is right here, just[br]right at the bottom.

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So it's gotta be like that.

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That's gotta be the x-axis.

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That could be the x-axis and[br]then the y-axis could be out

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here someplace.

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Just so you have a frame[br]of reference.

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

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Well, this is the point 5,[br]12, this is y equals 12.

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So what is this height?

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This is a radius.

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

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So the radius is equal to 12.

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

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well, the radius is 12.

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It's the y-coordinate.

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Next problem.

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Whoops.

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I say whoops a lot.

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Problem sixteen.

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They have this men, women,[br]woman, and then they say

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voting age population.

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So population, and then[br]registered, and they say 1200,

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1000, 1300, and 1200.

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They say, the table above gives[br]the voter registration

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data for the town of[br]Bridgeton at the

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time of a recent election.

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In the election, 40%[br]of the voting age

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population actually voted.

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So this is the voting[br]age population.

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And we know that 40%[br]actually voted.

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If the turnout for the election[br]is defined by the

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number who actually voted,[br]divided by registered, what

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was the turnout for[br]this election?

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So what's the number[br]who actually voted?

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It's 40% of the voting[br]age population.

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So what's the voting[br]age population?

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Well the total population[br]is the men and

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women, so that's 2500.

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Just add these two up.

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And what's 40% of 2500?

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That's 2500 times 0.4.

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Let's see.

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4 times 25 is 100.

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Two more zeros.

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0, 0.

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And then, of course,[br]one decimal.

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So it's 1000.

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I just took 40% of 2500.

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1000 people voted.

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

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the number voted, which is[br]1000, divided by the

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registered voters.

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

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so you add that up.

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That's 2200 total registered[br]voters.

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

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That's our answer.

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That's the fraction[br]that voted.

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That's what they wanted.

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

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fraction, 5/11.

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

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them mad there.

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See you in the next video.