PSAT 1.9 Math Diagnostic

PSAT 1.9 Math Diagnostic. What is the maximum size widescreen TV Abby can purchase?

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PSAT Math Diagnostic
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Transcript

00:19

three for a wide screen tv and width height ratio

00:22

is sixteen to nine Abby currently has a fifty five

00:25

inch standard sized tv you two space limitations in her

00:29

living room The new tv cannot be wider than her

00:31

current tv What is the maximum size widescreen tv that

00:36

abby can purchased and hear the pencil answer for everything

00:39

You whoever knew there could be so much math involved

00:43

in getting a new tv all poor abby wants to

00:45

do is plopped down on her couch and watch that

00:48

iron chef marathon well let's do her a solid and

00:51

figure this out for she's had a tough day Girl

00:53

needs to get her Relax on Okay so let's divide

00:56

and conquer here so we don't get overwhelmed by all

00:58

the numbers We're told that abby currently has a standard

01:01

sized tv with a wit toe height ratio for two

01:03

three And we're told that it's fifty five inch which

01:06

is measured diagonally triangles You really are everywhere aren't you

01:11

Well it looks like we're gonna have to pull that

01:13

old pit factory and the're amount of storage We can

01:16

call the width of abby's tv for x and the

01:18

height three act Since we know that's the ratio and

01:21

the hypothesis of our triangle is fifty five inches and

01:24

well that'll give us enough to work with using our

01:26

favorite serum we get for x in parentheses Squared plus

01:30

three x in parentheses Squared equals fifty five squared Now

01:35

let's actually square this stuff Well we get sixteen x

01:38

squared plus nine x squared equals three thousand twenty five

01:42

combined are like terms And twenty five x squared equals

01:45

three thousand twenty five Divide both sides by twenty five

01:48

to get x squared equals one hundred twenty one Then

01:51

take the square root of both sides and magically x

01:54

equals even number eleven We can plug that number back

01:58

into the unknown dimensions of abby's tv and looks like

02:01

it's forty four inches wide and thirty three inches high

02:04

Groovy Feels like we're getting somewhere which is always nice

02:07

now For abby's new tv we can do the same

02:10

thing here that we did for the old one except

02:13

we don't yet have the measure of the diagonal and

02:15

let's not forget that new ratio is a width of

02:17

sixteen to a height of nine so sixteen Acts in

02:20

parentheses Squared plus 9 x in princey squared equals c

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squared where c is the answer we're looking for i

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e the perfect size tv to fit in abby's television

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hole for lack of a better term we're going to

02:32

get two hundred fifty six x squared plus eighty one

02:35

x squared or three hundred thirty seven x squared equals

02:39

c squared from here we'll need to plug in each

02:41

of our answer choices and see what the largest possible

02:45

tv is that abby can get That won't force her

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Tio take out a wall All right we'll start with

02:51

a forty nine inches plugging in forty nine for sea

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We get three hundred thirty seven x squared equals forty

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nine square which is two thousand four hundred one Divide

03:00

both sides by three hundred thirty seven and x squared

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equals well Run around seven point one two Take the

03:05

square Root of both sides and x comes out to

03:07

about two point six six nine now we're looking for

03:10

the tvs with which is sixteen x so multiplying Two

03:14

point six six nine by sixteen we get roughly forty

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two point seven inches on that comes in under the

03:19

forty four inch requirement but well we wonder if we

03:22

can do any better plugging in fifty we get three

03:25

hundred thirty seven x squared equals fifty squared which is

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twenty five hundred Once we've divided both sides by three

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hundred thirty seven and taking the square root of both

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sides we get x equals two point seven two we'll

03:35

multiply that by sixteen and we end up with forty

03:38

three point five eight which is awfully close to that

03:40

forty four inch mark You could barely get a finger

03:43

in on either side enough if you want to go

03:45

sticking your fingers in there when we try the same

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thing with option c fifty one inches and we do

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all the busywork we find that fifty one inch tv

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would have a width of forty four point four five

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inches which ain't gonna work And if a fifty one

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inch tv is too big and a fifty two inch

04:01

tv and going to cut it either Which means that

04:03

the biggest possible tv abby can buy without having toe

04:06

learn how to maneuver A hacksaw is b fifty inches

04:09

You that was exhausting So let's not wake her more

04:13

things all tuckered out from listening to us Do all 00:04:16.222 --> [endTime] the work