[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.84,0:00:01.53,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:01.53,0:00:03.14,Default,,0000,0000,0000,,We're on problem\Nnumber twelve.
Dialogue: 0,0:00:06.57,0:00:13.88,Default,,0000,0000,0000,,The perimeter of a rectangular\Nplot of land is 250 meters.
Dialogue: 0,0:00:13.88,0:00:17.50,Default,,0000,0000,0000,,If the length of one side of the\Nplot is 40 meters, what is
Dialogue: 0,0:00:17.50,0:00:19.96,Default,,0000,0000,0000,,the area of the plot\Nin square meters?
Dialogue: 0,0:00:19.96,0:00:21.41,Default,,0000,0000,0000,,So let me draw a\Nrectangle here.
Dialogue: 0,0:00:26.96,0:00:32.19,Default,,0000,0000,0000,,We know that one side of\Nthe plot is 40 meters.
Dialogue: 0,0:00:32.19,0:00:33.05,Default,,0000,0000,0000,,Well it's a rectangle.
Dialogue: 0,0:00:33.05,0:00:35.21,Default,,0000,0000,0000,,So if this side is 40,\Nthen this side is
Dialogue: 0,0:00:35.21,0:00:37.44,Default,,0000,0000,0000,,also going to be 40.
Dialogue: 0,0:00:37.44,0:00:40.70,Default,,0000,0000,0000,,And let's say we don't\Nknow the other side.
Dialogue: 0,0:00:40.70,0:00:43.26,Default,,0000,0000,0000,,Well if this side is\Nx, this is also x.
Dialogue: 0,0:00:43.26,0:00:47.09,Default,,0000,0000,0000,,So what is the perimeter,\Nexpressed in these terms?
Dialogue: 0,0:00:47.09,0:00:52.75,Default,,0000,0000,0000,,What's 40 plus 40, which\Nis 80, plus x plus x.
Dialogue: 0,0:00:52.75,0:00:55.66,Default,,0000,0000,0000,,So if 80 plus 2x is the\Nperimeter, and we know that
Dialogue: 0,0:00:55.66,0:00:59.85,Default,,0000,0000,0000,,the perimeter is 250.
Dialogue: 0,0:00:59.85,0:01:04.35,Default,,0000,0000,0000,,And so solving for x we get 2x\Nis equal to, what's 250 minus
Dialogue: 0,0:01:04.35,0:01:07.92,Default,,0000,0000,0000,,80, that's 170.
Dialogue: 0,0:01:07.92,0:01:17.22,Default,,0000,0000,0000,,At that x is equal to 85.
Dialogue: 0,0:01:17.22,0:01:19.77,Default,,0000,0000,0000,,And now if we want to get the\Narea of this, we just multiply
Dialogue: 0,0:01:19.77,0:01:21.35,Default,,0000,0000,0000,,the base times the height.
Dialogue: 0,0:01:21.35,0:01:30.55,Default,,0000,0000,0000,,So 85 times 40, put a 0 here,\Nand 4 times 5 is 20.
Dialogue: 0,0:01:30.55,0:01:34.93,Default,,0000,0000,0000,,4 times 8 is 32, plus 2 is 34.
Dialogue: 0,0:01:34.93,0:01:39.74,Default,,0000,0000,0000,,So the area is 3400\Nsquare meters.
Dialogue: 0,0:01:39.74,0:01:41.65,Default,,0000,0000,0000,,I hope I didn't do something\Nwrong with the math, but I
Dialogue: 0,0:01:41.65,0:01:43.70,Default,,0000,0000,0000,,think you get the point.
Dialogue: 0,0:01:43.70,0:01:44.95,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:01:47.17,0:01:48.42,Default,,0000,0000,0000,,Problem thirteen.
Dialogue: 0,0:01:50.81,0:01:53.41,Default,,0000,0000,0000,,A school ordered $600 worth\Nof light bulbs.
Dialogue: 0,0:01:57.35,0:02:00.34,Default,,0000,0000,0000,,Some of the light bulbs cost $1\Neach, and others cost $2.
Dialogue: 0,0:02:00.34,0:02:02.91,Default,,0000,0000,0000,,So some were $1, some\Nwere $2 each.
Dialogue: 0,0:02:02.91,0:02:10.20,Default,,0000,0000,0000,,If twice as many $1 bulbs as\N$2 bulbs were ordered, how
Dialogue: 0,0:02:10.20,0:02:14.27,Default,,0000,0000,0000,,many light bulbs were ordered\Nall together?
Dialogue: 0,0:02:14.27,0:02:15.41,Default,,0000,0000,0000,,Fascinating.
Dialogue: 0,0:02:15.41,0:02:23.85,Default,,0000,0000,0000,,So let's let x equal\Nnumber of $1 bulbs.
Dialogue: 0,0:02:23.85,0:02:29.95,Default,,0000,0000,0000,,I could introduce a variable y,\Nbut I could just say that x
Dialogue: 0,0:02:29.95,0:02:34.49,Default,,0000,0000,0000,,is the number of $1 bulbs, and\Nwe know that twice as many $1
Dialogue: 0,0:02:34.49,0:02:36.73,Default,,0000,0000,0000,,bulbs as $2 bulbs\Nwere ordered.
Dialogue: 0,0:02:36.73,0:02:39.68,Default,,0000,0000,0000,,So how can I express the\Nnumber of $2 bulbs?
Dialogue: 0,0:02:43.85,0:02:46.09,Default,,0000,0000,0000,,Well we know that twice\Nas many $1 bulbs were
Dialogue: 0,0:02:46.09,0:02:47.22,Default,,0000,0000,0000,,ordered as $2 bulbs.
Dialogue: 0,0:02:47.22,0:02:49.53,Default,,0000,0000,0000,,So this would be\Nx divided by 2.
Dialogue: 0,0:02:49.53,0:02:53.47,Default,,0000,0000,0000,,There are half as many\N$2 bulbs as $1 bulbs.
Dialogue: 0,0:02:53.47,0:02:58.29,Default,,0000,0000,0000,,And we know that if we add up\Nthe total number of bulbs,
Dialogue: 0,0:02:58.29,0:02:59.64,Default,,0000,0000,0000,,well actually we don't know.
Dialogue: 0,0:02:59.64,0:03:04.40,Default,,0000,0000,0000,,So what is the total cost if we\Nget x $1 bulbs, and if we
Dialogue: 0,0:03:04.40,0:03:07.15,Default,,0000,0000,0000,,get x divided by 2 $2 bulbs?
Dialogue: 0,0:03:07.15,0:03:10.12,Default,,0000,0000,0000,,What is going to be the\Ntotal cost of this?
Dialogue: 0,0:03:10.12,0:03:13.14,Default,,0000,0000,0000,,Well, I'm going to get x $1\Nbulbs, and they're each going
Dialogue: 0,0:03:13.14,0:03:14.80,Default,,0000,0000,0000,,to cost $1.
Dialogue: 0,0:03:14.80,0:03:18.40,Default,,0000,0000,0000,,Plus, I'm going to get x over\N2 $2 bulbs, and they're each
Dialogue: 0,0:03:18.40,0:03:21.94,Default,,0000,0000,0000,,going to cost $2.
Dialogue: 0,0:03:21.94,0:03:26.04,Default,,0000,0000,0000,,And when I add it all up it's\Ngoing to equal $600.
Dialogue: 0,0:03:26.04,0:03:28.68,Default,,0000,0000,0000,,So x times 1 is, of course, x.
Dialogue: 0,0:03:28.68,0:03:32.06,Default,,0000,0000,0000,,And then x over 2 times 2,\Nthat's lucky that worked out,
Dialogue: 0,0:03:32.06,0:03:34.99,Default,,0000,0000,0000,,plus x is equal to $600.
Dialogue: 0,0:03:34.99,0:03:39.15,Default,,0000,0000,0000,,So 2x is equal to 600.
Dialogue: 0,0:03:39.15,0:03:41.78,Default,,0000,0000,0000,,x is equal to 300.
Dialogue: 0,0:03:41.78,0:03:44.46,Default,,0000,0000,0000,,And they want to know\Nhow many lightbulbs
Dialogue: 0,0:03:44.46,0:03:47.21,Default,,0000,0000,0000,,were ordered all together.
Dialogue: 0,0:03:47.21,0:03:54.65,Default,,0000,0000,0000,,So we got 300 $1 bulbs, and we\Ngot 1/2 as many $2 bulbs, x
Dialogue: 0,0:03:54.65,0:03:55.45,Default,,0000,0000,0000,,divided by 2.
Dialogue: 0,0:03:55.45,0:04:01.37,Default,,0000,0000,0000,,So we got 150 $2 bulbs.
Dialogue: 0,0:04:01.37,0:04:06.49,Default,,0000,0000,0000,,So together we got 450 bulbs.
Dialogue: 0,0:04:06.49,0:04:07.74,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:04:10.18,0:04:11.68,Default,,0000,0000,0000,,Image clear.
Dialogue: 0,0:04:14.24,0:04:18.85,Default,,0000,0000,0000,,I'll do it in a new color\Nso we don't get bored.
Dialogue: 0,0:04:18.85,0:04:20.55,Default,,0000,0000,0000,,Fourteen.
Dialogue: 0,0:04:20.55,0:04:32.44,Default,,0000,0000,0000,,If 4 times x plus y times x\Nminus y is equal to 40, and we
Dialogue: 0,0:04:32.44,0:04:36.66,Default,,0000,0000,0000,,also know that x minus y is\Nequal to 20, what is the value
Dialogue: 0,0:04:36.66,0:04:38.36,Default,,0000,0000,0000,,of x plus y?
Dialogue: 0,0:04:38.36,0:04:40.51,Default,,0000,0000,0000,,Well, we know x minus y is equal\Nto 20, so we can just
Dialogue: 0,0:04:40.51,0:04:41.54,Default,,0000,0000,0000,,substitute that right here.
Dialogue: 0,0:04:41.54,0:04:46.03,Default,,0000,0000,0000,,So then we get 4 times x plus y\Ntimes, instead of writing x
Dialogue: 0,0:04:46.03,0:04:51.51,Default,,0000,0000,0000,,minus y we can just write times\N20, is equal to 40.
Dialogue: 0,0:04:51.51,0:04:57.39,Default,,0000,0000,0000,,Or, if we multiply 20 times 4,\Nwe know that 80 times x plus y
Dialogue: 0,0:04:57.39,0:04:59.70,Default,,0000,0000,0000,,is equal to 40.
Dialogue: 0,0:04:59.70,0:05:03.24,Default,,0000,0000,0000,,Then we know, divide both sides\Nby 80, and we get x plus
Dialogue: 0,0:05:03.24,0:05:04.20,Default,,0000,0000,0000,,y is 40 over 80.
Dialogue: 0,0:05:04.20,0:05:06.90,Default,,0000,0000,0000,,Which is the same\Nthing as 1/2.
Dialogue: 0,0:05:06.90,0:05:08.06,Default,,0000,0000,0000,,And that's our answer.
Dialogue: 0,0:05:08.06,0:05:11.50,Default,,0000,0000,0000,,x plus y is equal to 1/2.
Dialogue: 0,0:05:11.50,0:05:12.75,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:05:16.00,0:05:17.25,Default,,0000,0000,0000,,Fifteen.
Dialogue: 0,0:05:19.26,0:05:21.42,Default,,0000,0000,0000,,In a rectangular coordinate\Nsystem, that's what we're
Dialogue: 0,0:05:21.42,0:05:26.60,Default,,0000,0000,0000,,familiar with, the center of a\Ncircle has coordinates 5, 12.
Dialogue: 0,0:05:26.60,0:05:32.59,Default,,0000,0000,0000,,So I draw a circle, and then the\Ncenter of the circle has
Dialogue: 0,0:05:32.59,0:05:35.84,Default,,0000,0000,0000,,the coordinates 5, 12.
Dialogue: 0,0:05:35.84,0:05:39.99,Default,,0000,0000,0000,,And the circle touches the\Nx-axis at one point only.
Dialogue: 0,0:05:39.99,0:05:41.58,Default,,0000,0000,0000,,What is the radius\Nof the circle?
Dialogue: 0,0:05:41.58,0:05:44.71,Default,,0000,0000,0000,,So it just touches the x-axis.
Dialogue: 0,0:05:44.71,0:05:47.19,Default,,0000,0000,0000,,And the only place where it can\Ntouch the x-axis only in
Dialogue: 0,0:05:47.19,0:05:48.84,Default,,0000,0000,0000,,one point is this exact.
Dialogue: 0,0:05:48.84,0:05:51.69,Default,,0000,0000,0000,,Because the x-axis is\Nessentially a horizontal line.
Dialogue: 0,0:05:51.69,0:05:53.87,Default,,0000,0000,0000,,And where else can you\Ntouch the x-axis?
Dialogue: 0,0:05:53.87,0:05:55.65,Default,,0000,0000,0000,,You could touch it\Nhere, on top.
Dialogue: 0,0:05:55.65,0:05:59.87,Default,,0000,0000,0000,,But if the x-axis was up here,\Nthen the y coordinate would
Dialogue: 0,0:05:59.87,0:06:00.94,Default,,0000,0000,0000,,not be positive.
Dialogue: 0,0:06:00.94,0:06:03.73,Default,,0000,0000,0000,,So this has a positive y\Ncoordinate, so we know it has
Dialogue: 0,0:06:03.73,0:06:07.30,Default,,0000,0000,0000,,to be above the x-axis,\Nit's at 12.
Dialogue: 0,0:06:07.30,0:06:10.69,Default,,0000,0000,0000,,So we know the only place where\Nyou can touch the x-axis
Dialogue: 0,0:06:10.69,0:06:13.85,Default,,0000,0000,0000,,just once is right here, just\Nright at the bottom.
Dialogue: 0,0:06:13.85,0:06:15.48,Default,,0000,0000,0000,,So it's gotta be like that.
Dialogue: 0,0:06:18.29,0:06:19.54,Default,,0000,0000,0000,,That's gotta be the x-axis.
Dialogue: 0,0:06:22.70,0:06:24.70,Default,,0000,0000,0000,,That could be the x-axis and\Nthen the y-axis could be out
Dialogue: 0,0:06:24.70,0:06:27.01,Default,,0000,0000,0000,,here someplace.
Dialogue: 0,0:06:27.01,0:06:28.61,Default,,0000,0000,0000,,Just so you have a frame\Nof reference.
Dialogue: 0,0:06:28.61,0:06:30.90,Default,,0000,0000,0000,,And if that's the x-axis,\Nthen what's the radius?
Dialogue: 0,0:06:30.90,0:06:39.92,Default,,0000,0000,0000,,Well, this is the point 5,\N12, this is y equals 12.
Dialogue: 0,0:06:39.92,0:06:41.31,Default,,0000,0000,0000,,So what is this height?
Dialogue: 0,0:06:41.31,0:06:42.98,Default,,0000,0000,0000,,This is a radius.
Dialogue: 0,0:06:42.98,0:06:44.45,Default,,0000,0000,0000,,Well that's just the\Ny-coordinate, it's 12.
Dialogue: 0,0:06:44.45,0:06:48.44,Default,,0000,0000,0000,,So the radius is equal to 12.
Dialogue: 0,0:06:48.44,0:06:49.79,Default,,0000,0000,0000,,They're just saying what is\Nthe radius of the circle,
Dialogue: 0,0:06:49.79,0:06:50.85,Default,,0000,0000,0000,,well, the radius is 12.
Dialogue: 0,0:06:50.85,0:06:52.89,Default,,0000,0000,0000,,It's the y-coordinate.
Dialogue: 0,0:06:52.89,0:06:54.14,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:06:56.71,0:06:58.20,Default,,0000,0000,0000,,Whoops.
Dialogue: 0,0:06:58.20,0:07:00.84,Default,,0000,0000,0000,,I say whoops a lot.
Dialogue: 0,0:07:00.84,0:07:02.09,Default,,0000,0000,0000,,Problem sixteen.
Dialogue: 0,0:07:04.41,0:07:11.61,Default,,0000,0000,0000,,They have this men, women,\Nwoman, and then they say
Dialogue: 0,0:07:11.61,0:07:13.48,Default,,0000,0000,0000,,voting age population.
Dialogue: 0,0:07:13.48,0:07:21.85,Default,,0000,0000,0000,,So population, and then\Nregistered, and they say 1200,
Dialogue: 0,0:07:21.85,0:07:30.34,Default,,0000,0000,0000,,1000, 1300, and 1200.
Dialogue: 0,0:07:30.34,0:07:33.29,Default,,0000,0000,0000,,They say, the table above gives\Nthe voter registration
Dialogue: 0,0:07:33.29,0:07:35.06,Default,,0000,0000,0000,,data for the town of\NBridgeton at the
Dialogue: 0,0:07:35.06,0:07:36.93,Default,,0000,0000,0000,,time of a recent election.
Dialogue: 0,0:07:36.93,0:07:40.28,Default,,0000,0000,0000,,In the election, 40%\Nof the voting age
Dialogue: 0,0:07:40.28,0:07:42.88,Default,,0000,0000,0000,,population actually voted.
Dialogue: 0,0:07:42.88,0:07:46.43,Default,,0000,0000,0000,,So this is the voting\Nage population.
Dialogue: 0,0:07:46.43,0:07:50.40,Default,,0000,0000,0000,,And we know that 40%\Nactually voted.
Dialogue: 0,0:07:50.40,0:07:53.36,Default,,0000,0000,0000,,If the turnout for the election\Nis defined by the
Dialogue: 0,0:07:53.36,0:08:02.99,Default,,0000,0000,0000,,number who actually voted,\Ndivided by registered, what
Dialogue: 0,0:08:02.99,0:08:05.00,Default,,0000,0000,0000,,was the turnout for\Nthis election?
Dialogue: 0,0:08:05.00,0:08:06.83,Default,,0000,0000,0000,,So what's the number\Nwho actually voted?
Dialogue: 0,0:08:06.83,0:08:10.31,Default,,0000,0000,0000,,It's 40% of the voting\Nage population.
Dialogue: 0,0:08:10.31,0:08:11.83,Default,,0000,0000,0000,,So what's the voting\Nage population?
Dialogue: 0,0:08:11.83,0:08:13.31,Default,,0000,0000,0000,,Well the total population\Nis the men and
Dialogue: 0,0:08:13.31,0:08:15.47,Default,,0000,0000,0000,,women, so that's 2500.
Dialogue: 0,0:08:15.47,0:08:16.74,Default,,0000,0000,0000,,Just add these two up.
Dialogue: 0,0:08:16.74,0:08:19.11,Default,,0000,0000,0000,,And what's 40% of 2500?
Dialogue: 0,0:08:19.11,0:08:26.11,Default,,0000,0000,0000,,That's 2500 times 0.4.
Dialogue: 0,0:08:26.11,0:08:26.47,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:08:26.47,0:08:29.80,Default,,0000,0000,0000,,4 times 25 is 100.
Dialogue: 0,0:08:29.80,0:08:30.59,Default,,0000,0000,0000,,Two more zeros.
Dialogue: 0,0:08:30.59,0:08:32.12,Default,,0000,0000,0000,,0, 0.
Dialogue: 0,0:08:32.12,0:08:35.71,Default,,0000,0000,0000,,And then, of course,\None decimal.
Dialogue: 0,0:08:35.71,0:08:39.37,Default,,0000,0000,0000,,So it's 1000.
Dialogue: 0,0:08:39.37,0:08:41.09,Default,,0000,0000,0000,,I just took 40% of 2500.
Dialogue: 0,0:08:41.09,0:08:42.95,Default,,0000,0000,0000,,1000 people voted.
Dialogue: 0,0:08:42.95,0:08:44.74,Default,,0000,0000,0000,,And if we want to know the\Nturnout, we just have to say
Dialogue: 0,0:08:44.74,0:08:47.57,Default,,0000,0000,0000,,the number voted, which is\N1000, divided by the
Dialogue: 0,0:08:47.57,0:08:49.39,Default,,0000,0000,0000,,registered voters.
Dialogue: 0,0:08:49.39,0:08:52.89,Default,,0000,0000,0000,,Well the registered voters,\Nthere's 1000 men, 1200 women,
Dialogue: 0,0:08:52.89,0:08:53.78,Default,,0000,0000,0000,,so you add that up.
Dialogue: 0,0:08:53.78,0:08:58.31,Default,,0000,0000,0000,,That's 2200 total registered\Nvoters.
Dialogue: 0,0:08:58.31,0:09:06.67,Default,,0000,0000,0000,,That's the same thing\Nas 10/22, or 5/11.
Dialogue: 0,0:09:06.67,0:09:07.36,Default,,0000,0000,0000,,That's our answer.
Dialogue: 0,0:09:07.36,0:09:09.41,Default,,0000,0000,0000,,That's the fraction\Nthat voted.
Dialogue: 0,0:09:09.41,0:09:10.56,Default,,0000,0000,0000,,That's what they wanted.
Dialogue: 0,0:09:10.56,0:09:12.52,Default,,0000,0000,0000,,To find to be the fraction, so\Nyou can write it as this
Dialogue: 0,0:09:12.52,0:09:14.63,Default,,0000,0000,0000,,fraction, 5/11.
Dialogue: 0,0:09:14.63,0:09:16.34,Default,,0000,0000,0000,,I'll see you in the next video,\Nhopefully I didn't make
Dialogue: 0,0:09:16.34,0:09:17.09,Default,,0000,0000,0000,,them mad there.
Dialogue: 0,0:09:17.09,0:09:19.09,Default,,0000,0000,0000,,See you in the next video.