Question

Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions:
The sum of the length and width must be 30 centimeters.
The height must be 3 centimeters less than the length.
The box should have the greatest possible volume.
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is If the length of the box is x, write an expression for the width in terms of x.

Answer 1

I have 8 more questions that go along with this one.... Please helpppp

Answer 2

"length of the box is x"
"sum of the length and width must be 30 centimeters"
so what is the width in terms of x? Take a guess plz?

Answer 3

(x)(l)=30?????

Answer 4

Sum means adding...

Answer 5

Oh wow... okay so x+l=30

Answer 6

Yes, so the width = ?

Answer 7

x..... 30/l???

Answer 8

remember u wrote x + width = 30 right? so....

Answer 9

30-x=width

Answer 10

That is the right answer :)

Answer 11

Ooh okay so now... If the length of the box is x, write an expression for the height in terms of x.

Answer 12

The height must be 3 centimeters less than the length. So...

Answer 13

length-3= height ?

Answer 14

So x-3=height

Answer 15

That is correct :)

Answer 16

Ah thank you. Ok only 7 more... Write a function f(x) that gives the volume of a box of length x in polynomial form.

Answer 17

Sorry I got 5 more min only. Is the box a cube?

Answer 18

Oh no... okay well it doesn't say.

Answer 19

Hmmm just length by itself is no good to calculate volume. sorry!

Answer 20

it says V=lwh

Answer 21

yes but u only get x...oh wait - is this part of the same question in the first post?

Answer 22

yes! (:

Answer 23

OK then use the width n height eqns from above and put them in V=lwh :)

Answer 24

(30-x)(x-3) ?

Answer 25

one more term....

Answer 26

wait is it: (30-width)(30-x)(x-3)

Answer 27

Where u get (x-3)?? x = length right?

Answer 28

No no no ignore the last one....

Answer 29

(30-x)(x-3) and u missed the length....

Answer 30

x is length... so (30-width)

Answer 31

So (30-width) (30-x) (x-3) (l)(w)(h)

Answer 32

express length in term of x pl

Answer 33

u said "x is length... "

Answer 34

Yeah... I think I am. 30-width=length. 30-x=width x-3=height. The x is length

Answer 35

"x is length... " "30-x=width" "x-3=height"

Answer 36

Im confused.... 30-x=width is 30-length=width, 30-width=x which is 30-width=length and x-3=height is length-3=height.

Answer 37

Put length, width n height ALL in terms of x pl

Answer 38

(30-x=w) (30-w=x) (x-3=h)

Answer 39

U want the V=lwh equation with ONLY x, NO other unknown ok?

Answer 40

no l, no w, no h, no =, nothing but x and numbers :)

Answer 41

Ok so how do I know what numbers to put in replace of w and h?

Answer 42

"x is length... " "30-x=width" "x-3=height"

Answer 43

So I choose the numbers randomly??

Answer 44

I have to go; here is it V=x(30-x)(x-3)

Answer 45

Oh okay. Thank you very much for your help!!!!!!! (: