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PSAT 1.29 Math Diagnostic 172 Views


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Description:

PSAT 1.29 Math Diagnostic. Which of the following statements is true?


Transcript

00:00

Thank you We sneak And here's your shmoop du jour

00:05

Brought to you by public transportation You may bring a

00:08

sandwich with you onto the subway but you're definitely not

00:11

goingto eat fresh All right Chavan is starting a new

00:16

job and wants to minimize her commuting costs She has

00:20

two options for communiqu drive or take the train Her

00:23

car's fuel economy is thirty two miles a gallon Job

00:26

is located 20 miles from the house And parking at

00:29

work cost two Fifty a day Javan could also take

00:32

public transportation and get to work She drive two point

00:35

five miles to the train station and pay three seventy

00:37

five each way from train barking its train station is

00:40

free Which of the following statements is true and hear

00:44

the pencil answers All right Really compared gas here Train

00:47

car All right well to drive or not to drive

00:51

That is the question here for us this really is

00:54

a no brainer Have you ever heard of anyone having

00:56

a bad case of the train rage But okay Sounds

00:59

like sherman is more concerned about the money aspect of

01:03

things and well we can respect that her driving costs

01:06

would be made up Of two factors the cost of

01:08

gas and the cost of parking Parking is two Fifty

01:11

a day Easy enough We're told that her jobs twenty

01:14

miles from her house assuming she's actually gonna be driving

01:17

back home each day and not passing out on a

01:19

cot in the break room That's forty miles of driving

01:22

each day she gets thirty two miles a gallon so

01:25

let's see how much he's gassing it up Well fortified

01:28

by thirty two is one point two five so she's

01:31

using one and a quarter gallons for each round trip

01:34

to and from the office We can write this now

01:36

is an equation The expression one point two five x

01:39

plus two point five or x is the price of

01:42

gas All right we'll let that idol remain there now

01:45

onto the train option there's still five miles of driving

01:48

involved two point five miles to the train station and

01:50

two point five miles back which will use up five

01:53

thirty seconds of a gallon of gas Want that in

01:55

a decimals form so it lines up with our previous

01:58

expression for driving We take five divided by thirty two

02:01

and we get point One five six to five Well

02:04

the train cost three seventy five each way or seven

02:07

Fifty total each day So the expression for the train

02:11

will be point one five sixty five x plus seven

02:16

point five we'd like to know when the cost of

02:18

each would be the same So let's set these two

02:20

equal to one another and just solve for x That

02:23

gives us one point two five x plus two point

02:25

five equals point one five sixty five x plus seven

02:28

point five we can start by subtracting two point five

02:31

from both sides to get one point Two five Acts

02:33

evil point 1:5 60 five x plus five then subtract point

02:37

one five six to five x from each side and

02:39

we wind up with one point o nine three seven

02:42

five x equals five don't by both sides by one

02:45

point nine three seven five and it looks like axe

02:48

comes out to win right around four point five seven

02:51

and would you look at that option d suggest that

02:53

if gas is more than four fifty seven a gallon

02:55

is cheaper to take the train we can double check

02:58

our work by plugging in a few values for acts

03:00

above and below the forfeit seven mark we'll see that

03:03

Yeah it totally checks out Well these are answer and

03:06

she even got the answer She was looking for an

03:08

even better She found something to do during her commute

03:11

to make the sun go buy a shame She's not 00:03:14.25 --> [endTime] big on crossword puzzle

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