ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


PSAT Videos 97 videos

PSAT 1.1 Math Diagnostic
312 Views

PSAT 1.1 Math Diagnostic. If a rabbit consumes 3 meals a day, how many grams of food will a rabbit consume in 7 days?

PSAT 1.8 Math Diagnostic
211 Views

PSAT 1.8 Math Diagnostic. What is one value of x?

PSAT 1.38 Math Diagnostic
180 Views

PSAT 1.38 Math Diagnostic. What is f(g(x))?

See All

PSAT 1.16 Math Diagnostic 200 Views


Share It!


Description:

PSAT 1.16 Math Diagnostic. What is the maximum number of pounds of Type A that Malcolm should buy?


Transcript

00:00

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

00:05

brought to you by coffee beans you wouldn't think they're

00:08

big fans of insult comedy but they're always getting roasted

00:13

A coffee shop sells two different types of coffee beans

00:16

Taipei is eight fifty a pound and type he is

00:18

nine twenty five pounds Malcolm wants to spend no more

00:21

than a hundred bucks on coffee beans I'd also like

00:24

at least fifty five percent of the coffee beans he

00:26

purchases to be type a rounded to the nearest tenth

00:30

of a pound How many pounds of type asian Malcolm

00:32

by and here the tensile answer signed five six seven

00:37

hey if someone's personality khun b type a why not

00:39

a coffee bean We're sure they're some of them out

00:42

there who are overly ambitious workaholics and well what can

00:45

we say They love the grind So behind door number

00:48

one we've got this type a product selling for eight

00:50

fifty a pound and behind door number two there's a

00:53

type b being going for nine twenty five pounds malcolm

00:57

have one hundred bucks spending limit but he's also got

00:59

a really weird thing about needing at least fifty five

01:03

percent of his purchase To be the type a variety

01:06

we want to know the maximum number of pounds of

01:09

the type a b malcolm should buy How do we

01:11

get there Well it always helps to turn word problem

01:14

data into an equation here in math lands Unless you

01:17

do that we use the variable a fur type a

01:21

beans and b for type b b eight point five

01:24

a plus nine point two five evils one hundred In

01:27

other words than dollar amounts of all of the type

01:30

a beans malcolm buys lost the dollar amount of all

01:33

the type b b t vise will equal one hundred

01:36

bucks However we have to fiddle with things here because

01:39

malcolm's bizarro fifty five percent requirement dividing the number of

01:43

pounds for type a beans by the total number of

01:45

pounds should give us a number greater than or equal

01:48

to point five five so a over the total pounds

01:51

equals point five five The total number of pounds will

01:54

be equal to a lost be so we can rewrite

01:57

as a over the quantity A plus b equals point

02:01

Five five Well would you look at that We've got

02:04

ourselves a system of equation now we can start by

02:08

taking that first equation and isolate a so we'll start

02:11

by subtracting nine point two five b from both sides

02:14

then divide both sides by eight point five to get

02:17

a equals The quantity one hundred minus nine point two

02:20

five b all over eight point five second inequality lather

02:24

rinse repeat we'll multiply both sides by the quantity a

02:27

plus b to get playing people's point five five a

02:30

plus point five five d you still got an a

02:33

on both sides of the equation though so we'll have

02:35

to do something about that Let's subtract point five five

02:38

a from both sides to get a point Four five

02:40

day equals point five Five b and finally divide both

02:44

sides by point for five to get a equals point

02:47

Five five feet over Point for five now that all

02:51

that's out of the way we can put on our

02:53

substitution pants we've now determined that one hundred minus nine

02:56

point two five feet over eight point five is the

02:58

same as point five five feet over point four five

03:02

so we'll set them equal to one another We'll multiply

03:05

both sides by eight Point five to get rid of

03:07

the fraction on the left which gives us one hundred

03:09

minus nine point two five equals four point six seven

03:13

five beef over point four Five Now to get rid

03:17

of that fraction on the right we multiply both sides

03:20

by point four five and wind up with forty five

03:22

minus four point one six to five b equals four

03:25

point six seven five feet add four point one six

03:29

to five feet of both sides and who were getting

03:31

so close we can feel it We're left with forty

03:34

five people's eight point eight three seven five feet Then

03:37

divide both sides by forty five and we get b

03:40

equals five point o nine But keep in mind that

03:43

we just found the value of b the malcolm should

03:46

purchase around five point one pounds of the type b

03:49

being the type a which rules out option a instead

03:52

Let's take the five point o nine we just arrived

03:55

at and see what we get when we plug that

03:57

into our first inequality Well yet eight point five eight

04:01

last nine point two five times five point o nine

04:05

equals one hundred multiplying Through way get eight point five

04:08

a plus forty seven point Oh eight equals one hundred

04:12

and then we can subtract forty seven point oh eight

04:15

from both sides Get eight point five a equals fifty

04:19

two point ninety two Divide both sides by eight point

04:22

five and looks like a comes out to about six

04:24

point two two five which when we round that psych

04:27

rock comes out tio six point to option c we

04:31

can double check our numbers by figuring out how much

04:33

these things are gonna run Malcolm well six point two

04:36

times the eight fifty that it cost per pound comes

04:39

out fifty two dollars and seventy cents and five point

04:42

o nine times nine twenty five equals forty seven point

04:46

eight Well if we had those two together we get

04:48

ninety nine dollars seventy eight cents which will leave mouth

04:52

um twelve cents left over to buy himself something nice

Related Videos

Secret Ingredients
391 Views

PSAT 1.3 Math Narrative Walkthrough. How many full packages of secret ingredient does the company have to buy to make one 50-gallon batch?

PSAT 1.1 Reading Diagnostic
1006 Views

PSAT 1.1 Reading Diagnostic. The main purpose of the first two paragraphs is to...what?

PSAT 2.2 Reading Diagnostic
379 Views

PSAT 2.2 Reading Diagnostic. What is the main rhetorical effect of this phrase in the second paragraph?

PSAT 1.3 Writing Diagnostic
282 Views

PSAT 1.3 Writing Diagnostic. To make the paragraph most logical, sentence 2 in the second paragraph should be placed...where?

PSAT 1.4 Writing Diagnostic
239 Views

PSAT 1.4 Writing Diagnostic. Which choice most effectively combines the two sentences in the underlined portion?