Word problem help.

[spyke100]

I've tried this problem numerous times different ways and it seems the more I try it the more problems I come across. Anyway.

David's room is 12ft by 15ft. He wants to leave a uniform strip of floor around the rug and can afford to buy 108ft² of carpeting. What dimensions should the rug have?

I've included a little illustration as to what it looks like (in my eyes). How would you solve this?
[attachment=0:3mvurz8m]mat.png[/attachment:3mvurz8m]

 

[Deleted member 4993]

I've tried this problem numerous times different ways and it seems the more I try it the more problems I come across. Anyway.

David's room is 12ft by 15ft. He wants to leave a uniform strip of floor around the rug and can afford to buy 108ft² of carpeting. What dimensions should the rug have?

I've included a little illustration as to what it looks like (in my eyes). How would you solve this?
[attachment=0:2cg0e5cd]mat.png[/attachment:2cg0e5cd]

I would first define variable - things to find out.

The width of the carpet = x

Then I would calculate the "uncarpeted" area as a function of 'x'...................................(1)

Then I would find the expression for carpeted area by subtracting (1) from (12*15=)180 ............................(2)

Then I would set (2) to be less than 108 - and solve for 'x'.

How about that .............................................................

 

[spyke100]

I've tried this problem numerous times different ways and it seems the more I try it the more problems I come across. Anyway.

David's room is 12ft by 15ft. He wants to leave a uniform strip of floor around the rug and can afford to buy 108ft² of carpeting. What dimensions should the rug have?

I've included a little illustration as to what it looks like (in my eyes). How would you solve this?
[attachment=0:32zcf1pp]mat.png[/attachment:32zcf1pp]

I would first define variable - things to find out.

The width of the carpet = x

Then I would calculate the "uncarpeted" area as a function of 'x'...................................(1)

Then I would find the expression for carpeted area by subtracting (1) from (12*15=)180 ............................(2)

Then I would set (2) to be less than 108 - and solve for 'x'.

How about that .............................................................

The difficulty I'm coming across is modeling step (1).... Like i said, Ive been looking at this problem for hours, literally, and I am not really sure what is right any more.

 

[Deleted member 4993]

I've tried this problem numerous times different ways and it seems the more I try it the more problems I come across. Anyway.

David's room is 12ft by 15ft. He wants to leave a uniform strip of floor around the rug and can afford to buy 108ft² of carpeting. What dimensions should the rug have?

I've included a little illustration as to what it looks like (in my eyes). How would you solve this?
[attachment=0:2t6ccj0y]mat.png[/attachment:2t6ccj0y]

I would first define variable - things to find out.

The width of the carpet = x

Then I would calculate the "uncarpeted" area as a function of 'x'...................................(1)

Then I would find the expression for carpeted area by subtracting (1) from (12*15=)180 ............................(2)

Then I would set (2) to be less than 108 - and solve for 'x'.

How about that .............................................................

The difficulty I'm coming across is modeling step (1).... Like i said, Ive been looking at this problem for hours, literally, and I am not really sure what is right any more.

Please show us what you have tried - even if it is wrong - so that we know where to start.

 

[spyke100]

Well so far here is what I have in mind...

(15-x)(12-x)=180-108

300 - 27x - x²= 72
-72 -72
_______________
208 - 27x - x²

-------> From here I draw a blank in my head......

 

[Denis]

Can you "see" that sides of inside rectangle are 12-2x and 15-2x? With area 108 sq.ft.

You seem to be complicating something simple.

 

[Denis]

Well so far here is what I have in mind...
(15-x)(12-x)=180-108
300 - 27x - x²= 72
-72 -72
_______________
208 - 27x - x²
-------> From here I draw a blank in my head......

Spyke, what are you doing?
(15-x)(12-x) = 180 - 27x + x^2 ; NOT 300 - 27x - x^2

Are you just tired, or do you not know how to do these?

 

[Deleted member 4993]

Denis is correct.

I misread the problem.

The inside rectangle is the carpeted area (due to temporary insanity - I thought the outside area was being carpeted).

So then

width of the carpet = 12 - x - x = 12 - 2x

Length of the carpet = 15 - x - x = 15 - 2x

Then - what is the area of the carpet? ----- (12 - 2x ) * (15 - 2x )

That must be less than 108

You'll get a Quadratic inequality

.... and continue.

 

[Denis]

The inside rectangle is the carpeted area (due to temporary insanity - I thought the outside area was being carpeted).

Well, don't get a side job installing carpet :shock: