Question

Plz help i will give medal and i will fan ^~^

Answer 1

A company makes rugs in two sizes. A small size rug requires 2 hours for dyeing and 4 hours for knotting. A medium size rug requires 3 hours for dyeing and 6 hours for knotting. The company's dyeing unit cannot work for more than 40 hours in a week, and the knotting unit cannot work for more than 50 hours in week. Let S represent the number of small size rugs that the company can manufacture in a week and M represent the number of medium size rugs that the company can manufacture in a week. Which of the following statements best explains whether the company will be able to make 12 small size rugs and 5 medium size rugs in a week?

The company will not be able to make these numbers in a week because of the system restrictions of 2S + 3M ≤ 40 and 4S + 6M ≤ 50.

The company will be able to make these numbers in a week because of the system restrictions of 2S + 4S ≤ 40 and 3M + 6M ≤ 50.

The company will be able to make these numbers in a week because of the system restrictions of 4S + 3M ≤ 40 and 2S + 6M ≤ 50.

The company will not be able to make these numbers in a week because of the system restrictions of 2S + 3S ≤ 40 and 4M + 6M ≤ 50.

Answer 2

A small size rug requires 2 hours for dyeing
A medium size rug requires 3 hours for dyeing

Give a "name" to the number of small rugs. Call it S
similarly call the number of medium rugs M

how many hours does it take to dye S small rugs?
any idea ?

Answer 3

10 hours

Answer 4

how did you get 10 ?

Answer 5

I thought i said 5 not S s and 5 look the same on my screen

Answer 6

so you did 2*5 ?

that is the right idea. except use S instead of 5
multiply a number times a letter is easy. you just write down 2*S (or in algebra where we leave out the multiply sign) : 2S

Answer 7

A medium size rug requires 3 hours for dyeing
call the number of medium rugs M
how many hours does it take to dye M medium rugs?

Answer 8

3 hours

Answer 9

per medium rug. But you have "M" of these rugs

Answer 10

remember M is an (unknown) number.

Answer 11

Ok

Answer 12

if you knew the number you know what to do to find the total number of hours?
what would you do ?

Answer 13

A medium size rug requires 3 hours for dyeing
if you had 2 medium rugs, how long to dye both of them?

Answer 14

6

Answer 15

now here is the idea: the number 6 is not the important thing. What is important is how did you get the 6. what did you do to find 6?

you did 3 hours per rug times number of rugs

that is the idea: 3 * # of rugs

and if we have the number of rugs= M
how long to dye M medium rugs?

Answer 16

idk 3

Answer 17

the idea: 3 * # of rugs

Do you get the idea that "M" is the number of rugs ? We can give names to numbers

for example if you had a dozen rugs and it takes 3 hours to dye each rug
it will take 3 * dozen hours

dozen is just a name.

But we can use M as a name.

Answer 18

So the answer is C

Answer 19

im just doin process of elimintion

Answer 20

Do you have time to learn how to do this? It will take some time.

Answer 21

Yea i have the time

Answer 22

so let's see if this part makes sense:
It takes 3 hours to dye a rug. To find how long it takes to dye 1, 2 or 3 rugs:

It takes 1*3 hours to dye 1 rug
It takes 2*3 hours to dye 2 rugs
It takes 3*3 hours to dye 3 rugs

Answer 23

K

Answer 24

do you see a pattern?

Answer 25

1*3
2*3
3*3

how long to dye 4 rugs?
4*3

notice we do not have to multiply it out to get a number. we just write
4*3

Answer 26

Yea

Answer 27

now don't multiply it out, just write it down. How long to dye 5 rugs?

Answer 28

5

Answer 29

i mean it takes 3

Answer 30

we have a pattern:
1*3
2*3
3*3
4*3

the pattern will be the same for 5 rugs. try again

Answer 31

5*3

Answer 32

now think about that. you wrote
5*3

that means 5 rugs will take 5*3 hours
if we simplify that we get 15 hours

does that seem right?

Answer 33

yea because it is the same patteren for the rest of the rugs

Answer 34

yes, it is correct.

Answer 35

how long to dye 6 rugs? (don't multiply it out, just write it down)

Answer 36

Wrote it

Answer 37

write it here

Answer 38

oh 6*3

Answer 39

we have a pattern:
1*3
2*3
3*3
4*3
5*3
6*3

what about 7 rugs?

Answer 40

7*3

Answer 41

now, what if we use a letter instead of a number? say we have M rugs

we follow the pattern

how many hours for M rugs?

Answer 42

m*3

Answer 43

yes.

Now that is the main idea. The pattern is the same whether we use numbers or letters.

Answer 44

we use that pattern to answer this:

A medium size rug requires 3 hours for dyeing
call the number of medium rugs M


how many hours does it take to dye M medium rugs?

Answer 45

M*3

Answer 46

yes.

does this make any sense?

Answer 47

can you answer this question

A small size rug requires 2 hours for dyeing
you have S small rugs

how long to dye S small rugs?

Answer 48

S*2

Answer 49

exactly

Answer 50

now how long does it take to dye both the small rugs and the medium rugs?

we write down the sum. can you do that?

Answer 51

So you want me to put S * 2 = M * 3

Answer 52

almost. but they are not equal

we want to add them together. The best we can do is put a + sign between them (which means "add together")

Answer 53

S * 2 + M * 3

Answer 54

Like that

Answer 55

yes. that is the total number of hours to dye the small and medium rugs

Answer 56

it is the "math" way to say the sum of hours for the small rugs and the medium rugs

Answer 57

dyeing unit cannot work for more than 40 hours in a week,

that means the sum (i.e. S * 2 + M * 3 ) must be less than or equal to 40

can you write that use ≤ ?

Answer 58

<

Answer 59

:P

Answer 60

S * 2 < M * 3

Answer 61

less than or equal uses ≤
less than uses <

hours ≤ 40

Answer 62

not S * 2 < M * 3

we worked hard to write down the sum of the hours as
S*2 + M*3

think of that as a thing (it is a thing, it is the sum of the hours it takes to dye the rugs)

and we know that the sum must be less than or equal to 40

Answer 63

Ok

Answer 64

we say the
hours to dye the rugs is less than or equal to 40

now write that in "math"
the hours to dye the rugs is S*2 + M*3
less than or equal is ≤
40 is 40

can you write it out in "math"?

Answer 65

Umm lol not really

Answer 66

math is a "short-hand" way to write the English.

replace the words with the "short version"
in other words, use
the hours to dye the rugs is S*2 + M*3
less than or equal is ≤
40 is 40

to replace the words in
hours to dye the rugs is less than or equal to 40

Answer 67

example:

number of people is less than 40

long version short version
number of people is X
is less than is ≤
40 is 40

using the short version, we write
X ≤ 40

Answer 68

long version short version
the hours to dye the rugs is S*2 + M*3
is less than is ≤
40 is 40

Answer 69

O ok

Answer 70

give it a try

Answer 71

40 < S * 2 + M * 3

Answer 72

almost. that says that the hours to dye is more than 40
the "bigger" side is next to the bigger side of <
we want the hours to be less than 40

Answer 73

40 > S * 2 + M * 3

Answer 74

yes.

but we should tweak that. we want hours is less than OR EQUAL
we should write it
40 ≥ S * 2 + M * 3
or
40 >= S * 2 + M * 3

Answer 75

also, we can put the S * 2 + M * 3 first (as along as we write the 40 next to thebigger side of >)

in other words, we can also write
S * 2 + M * 3 ≤ 40

Answer 76

remember in algebra we usually don't write the multiply sign, and we usually put letters after numbers (don't have to, but it is a habit people use)

so
S * 2 + M * 3 ≤ 40
can be written as
2S + 3M ≤ 40

The answer must have this relation in it.

Answer 77

can you find any choices with that relation?

Answer 78

A

Answer 79

yes, and the other choices do not. so A is the only possible choice.

Answer 80

^~^ thx soooo MUCH for your time to help me out phi

Answer 81

yw