Thread: Expressing Area in terms of Width

1. Expressing Area in terms of Width

I'm having trouble with wear to start on this problem, help!

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 3 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.

2. Originally Posted by Togechu64
I'm having trouble with wear to start on this problem, help!

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 3 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.

Always draw a picture for stuff like this

Calling the bottom of the poster w, for width, we see that the width of the printed area is w-10-10=w-20 because of the 10cm margin on both sides

Then the side is l, for length, and because of the margin the length of the printed area is l-3-3=l-6

Since the whole poster has area of 500, $lw=500$ so $l=\frac{500}{w}$

so you can substitute that into our equations to get the length in terms of the width

Then multiply them together for the printed area expression

3. Ok so what I got was [(500/w)-(6)] X [w-20], but its still saying that its not correct, did I do something wrong?

4. Originally Posted by Togechu64
Ok so what I got was [(500/w)-(6)] X [w-20], but its still saying that its not correct, did I do something wrong?

I'm sorry I think I misread the question

"there is a margin around the edges of 10cm at the top and 3 cm on the bottom and sides"

this should mean that the only border of 10 cm is the top one, and all others are 3cm

the reason from before holds but the numbers should be slightly altered.
Try to give it a shot before I tell you how to do it

(I would argue this is a stupid setup, as the printing area will not be centered, which is probably why I glanced over this point beforehand, but whatever)

5. Well, that would mean that it would be [(500/w)-9] x [w-10], right? That was not the correct answer either.

6. Originally Posted by Togechu64
Well, that would mean that it would be [(500/w)-9] x [w-10], right? That was not the correct answer either.

No.

The length of the poster is L. There is a 10cm margin at the top and a 3cm margin at the bottom (if I am interpretting correctly)

So the printed area's length is L-10-3=L-13

The width of the poster is W. There is a 3cm margin on both the left and right sides of the poster. So the printed area's width is w-3-3=w-6

and lastly LW=500

so....

7. Haha sorry, I mistyped my numbers on that last post, I meant to say:

[(500/w)-6] x [w-13], but I just realized from your last post that I switched the two numbers by accident. Thank you very much, I got the right answer

8. Originally Posted by Togechu64
I'm having trouble with wear to start on this problem, help!

A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 10 cm at the top and 3 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.
hard to understand without a diagram

9. Originally Posted by ukorov
hard to understand without a diagram