# Express the length y of the building as a function of the width x

1. Aug 22, 2013

### lolilovepie

1. The problem statement, all variables and given/known data

A small office unit is to contain 500 feet sq of floor space.

(a) Express the length y of the building as a function of the width x.

(b) If the walls cost $100 per running foot, express the cost C of the walls as a function of the width x. (Disregard the wall space above the doors and the thickness of the walls.) 2. Relevant equations 3. The attempt at a solution I kept getting a different answer then the back in the book. :\ (a) Area=xy, so 500=xy, y=500/x (b) Perimeter=2(x+y), so perimeter=2(x+500/x)=2((x^2+500)/x). The cost C is$100*perimeter, so C=$100*2((x^2+500)/x)=200((x^2+500)/x) Last edited by a moderator: Aug 23, 2013 2. Aug 22, 2013 ### haruspex To help you we need to see your working, not the correct working from the book. 3. Aug 23, 2013 ### symbolipoint The book's answers mostly ARE the steps. They should be understandable. 4. Aug 23, 2013 ### HallsofIvy Staff Emeritus This is the answer in the book? If you keep getting a different answer, we can't tell you what you did wrong unless you tell us what you did! 5. Aug 23, 2013 ### lolilovepie This part is my work listed below! not the answer from the book! (sorry for the confusion) : (a) Area=xy, so 500=xy, y=500/x (b) Perimeter=2(x+y), so perimeter=2(x+500/x)=2((x^2+500)/x). The cost C is$100*perimeter, so C=\$100*2((x^2+500)/x)=200((x^2+500)/x)

6. Aug 23, 2013

### Staff: Mentor

What's the answer that's given in the book?

I didn't realize that the above was your work (your OP wasn't clear on this), so I will rescind the notification I gave you earlier.

7. Aug 23, 2013

### haruspex

As you may have judged from the responses so far, we all agree with your working! What is the answer in the book?
Btw, I notice it says "Disregard the wall space above the doors". Are you told the number and width of the doors, or should it say "disregard that some wall will be displaced by doors"?

8. Aug 23, 2013

### lolilovepie

The answer in the book was a) y(x)=500/x b) c(x)=300x+(100,000/x) -600

it also came with this image (forgot to post it) : http://tinypic.com/r/2d9w9xk/5

9. Aug 23, 2013

### lolilovepie

sorry, it also came with this picture that i forgot to post : http://tinypic.com/r/2d9w9xk/5
yeah , that's all it say

10. Aug 23, 2013

### Ray Vickson

Your computation of wall material length (what you call the perimeter) does not match the diagram. Start again!