# Word Problem Help

• Jun 4th 2009, 10:11 PM
gold4fools
Word Problem Help
Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

l-8= length of the yard(not border)
w-8= width of the yard(not border)

l= length of flower border
w= width of flower border

After that I wrote down my two equations:

lw-667= 548 and (l-8)(w-8)= 1215

I am stuck right now as I do not know what to do after simplifying both equations to:

lw= 1215 and lw-8l-8w+64=1215

Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.
• Jun 4th 2009, 10:28 PM
Quote:

Originally Posted by gold4fools
Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

l-8= length of the yard(not border)
w-8= width of the yard(not border)

l= length of flower border
w= width of flower border

After that I wrote down my two equations:

lw-667= 548 and (l-8)(w-8)= 1215

I am stuck right now as I do not know what to do after simplifying both equations to:

lw= 1215 and lw-8l-8w+64=1215

Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.

You are given 2 equations here :

$\displaystyle wl=1215$ ---1

$\displaystyle wl-8l-8w+64=1215$ ---2

From 1 , we can write it this way : $\displaystyle w=\frac{1215}{l}$

Then substitute into 2 , giving

$\displaystyle \frac{1215}{l}-8l-8\frac{1215}{l}+64=1215$

$\displaystyle 1215-8l^2-9720+64l=1215l$

$\displaystyle -8505-8l^2-1151l=0$

Can you solve this quadratic equation for l , then look for w .

Is this what u want to know ?
• Jun 4th 2009, 10:33 PM
VonNemo19
Quote:

Originally Posted by gold4fools
Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

l-8= length of the yard(not border)
w-8= width of the yard(not border)

l= length of flower border
w= width of flower border

After that I wrote down my two equations:

lw-667= 548 and (l-8)(w-8)= 1215

I am stuck right now as I do not know what to do after simplifying both equations to:

lw= 1215 and lw-8l-8w+64=1215

Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.

$\displaystyle lw=667$ and $\displaystyle (l+8)(w+8)-667=548$

Solve for l or w in one of these equations

$\displaystyle (l+8)(w+8)-667=548$
$\displaystyle (l+8)(w+8)=1215$
$\displaystyle l=\frac{1215}{w+8}-8$

now substitute
$\displaystyle [\frac{1215}{w+8}-8]w=667$

the rest is easy. just make the radius of your circle as long as half of the diagonal of the rectangle, find the area, and then subtract 1215 grom that area to find the wasted water.