Question

The volume of a fudge tin meust be 120 cm^3. The tin is 7cm longer than it is wide and six times longer than it is tall. Find the dimenmsions of the tin

Answer 1

l = w + 7
h = 6 * l = 6 * (w + 7)
Area = w * l * h = 120

Answer 2

Alright, so here the shape of the tin would be a rectangular prism.

Let w represent the width, (w + 7) represent the length, and then the height would be the length divided by 6 because the tin is six times longer than it is wide. Now the volume is
120 cm³, thus\[w(w +7)\left( \frac{ w +7 }{ 6 } \right)=120\]because the volume of a rectangular prism is the product of the area of the base and the height.

Sorry it took so long but my server always gives me problems!!!

Answer 3

@kris10 do you understand the equation and do you know how to solve it now?

Answer 4

so
i'll just find the value of w
and calculate each

Answer 5

isn't it (6)(wt7)

Answer 6

yes! Why don't you tell me what the value of w is here so that I know you did it correctly.

Answer 7

No to (6)(wt7)!

Answer 8

Think about it! The question states that ...it is six times longer than it is tall. This implies that the length is greater than the height. However, if the height is 6(w + 7) then that makes the tin taller than the length. So 6(w + 7) for the height is wrong!!! For example, suppose that the the height is 10, the the length would be (6)(10) because it is six times longer than it is tall. Now if the length is 60, then to get the height, you would divide the length by 6. Do you understand @kris10 ?

Answer 9

ok

Answer 10

OK so what is your answer? What is w?

Answer 11

What are the dimensions? Length, width, and height?

Answer 12

A=(w^3+14w^2+49)/(6)

Answer 13

It's not A for area!!! You mean to say V for volume! Where are you getting A from?

Answer 14

ok

Answer 15

Also your expanded form is incorrect because the last term in that trinomial should be 49w, NOT 49.

Answer 16

Now do you know how to solve the equation?

Answer 17

yeah
i saw the difference

Answer 18

OK so did you get the correct answer then?

Answer 19

[6(120)]-49=w(w+7)^2

Answer 20

What?? HUH?? Please try again!

Answer 21

i'm confused on how to get the value of w

Answer 22

\[w(w +7)\left( \frac{ w +7 }{ 6 } \right)=120\]Multiply both sides by 6 to obtain\[w(w +7)(w +7)=720\]Expand the left side and subtract 720 from both sides to obtain\[w ^{3}+14w ^{2}+49w -720=0\]Now apply the factor theorem to solve for w. @kris10 can you take it from here?

Answer 23

Try positive factors of 720 for w, to see which one makes the left side zero.

Answer 24

For example, the equation does not equal zero if w equals 1, 2, 3, or 4. Now you try 5 because it is the next factor of 720.

Answer 25

i don't know
i'm really getting headache with this

Answer 26

So we have

w³ + 14w² + 49w - 720 = 0

If w = 5, then

5³ + 14(5)² + 49(5) - 720 = 125 + 350 + 245 - 720 = 0

∴ the width is 5 cm, the length is 12 cm, and the height is 2 cm.


@kris10 do you understand?

Answer 27

yeah that's the answer but
how do you derived that 5

Answer 28

where did you get that 5

Answer 29

I already explained above that you have to try positive factors of 720.

Answer 30

Have you never learned the factor theorem? You would have had to in order to be assigned this question.

Answer 31

step by step in getting the 5 as the value of w

Answer 32

ok thanks a lot
thank you for helping

Answer 33

So you get it then?

Answer 34

can u help me in the next question

Answer 35

Sure, as long as it doesn't take as long as this one. Only because I have to go, otherwise I wouldn't mind that you take all the time it takes to understand.

Answer 36

ok

Answer 37

The clothes adds a 75% mark up to the wholesale price of merchandise to determine the selling price. If a jacket that costs $100 wholesale is on sale for 20% off, what could a customer pay for it?

Answer 38

OK so first you tell me what you think we should do because even though I'm in a rush, as a teacher, I can't just keep giving you the answers. So go ahead and tell me what you think we should do.

Answer 39

the price of the jacket? i think

Answer 40

OK look, just relax. I'll walk you through.

First we're told that there is a markup of 75% to the wholesale price to determine the selling price, right? So first we setup an equation that represents the selling price. Reread the first sentence of the problem and literally translate the English sentence into a mathematical statement (equation). What do you gather the equation is?

Answer 41

price=$100*(75%+20%)

Answer 42

No, forget about the 20% right now. Just concentrate on the first sentence. What is the equation for the selling price? You can't do the entire question in a single step.

Answer 43

Selling price=wholeprice+75%

Answer 44

Close! It's

Selling Price = wholesale + 75% of wholesale

Let P represent the selling price and W represent the wholesale price, the the equation should be

P = W + 0.75W

OR

P = 1.75W

Understand?! Convert the percent to decimal.

Answer 45

Now utilize the second sentence of the problem. So what do you think we should do now?

Answer 46

my answer is to to it heheh
yes. . . i understand

Answer 47

selling price($100x20%)

Answer 48

No, remember that

P = 1.75W

Now the second sentence of the problem vocalizes that the jacket costs $100 wholesale and is on sale for 20% off so then we'll let the D represent the dicounted price, which is the price that the customer will pay. First if the wholesale price is $100, then the regular price P is

P = 1.75(100) or $175

Now if the discount applied is 20% to the regular price, then

D = 175 - 20% of 175

OR

D = 175 - 0.20(175)

D = 175 - 35

D = 140

∴ the customer pays $140 for the jacket after the discount.


Understood?

Answer 49

thanks a lot

Answer 50

So you're good with it then?

Answer 51

a little bit
thank you so much SIR