Math gurus - I could use some help!

[angelraven]

I'm helping my sister with a math problem. We keep arguing about it. lol

The problem goes like this:

You have a field with a perimeter of 852 ft, the length is twice the width. you cut down some trees to expand the field and add 40 ft to the legnth and 20 ft to the width. What's the difference in area between the old field and the new field?

Thanks for your help!

[AHammer]

let's see... if the width = x, then

perimeter = 852 = x + x + 2x + 2x = 6x

so width = 142 ft and length = 284 ft

old area = 40328 ft^2

expanded dimensions --> width = 162 ft and length = 324 ft

new area = 52488 ft^2

so difference in area 52488 - 40328 = 12160 square feet

i think

eta corrections in red

[karlatta]

Use these equations to find the original length and width:

2L + 2W = 852 (length + length + width + width = perimeter)
L = 2W (length is twice the width)

Sub in 2W everywhere there was an L in the first equation to get:
2(2W) + 2W = 852
4W + 2W = 852
6W = 852
W = 142

So then, L = 2W, or L = 2(142), or L = 284

Once you get that, you'll be able to figure out the old field's area. Then add 40 to the length and 20 to the width to get the new area. Then subtract!

(The math teacher in me can't bring myself to work the whole thing for you. :) )

[junkinmytrunk]

cringing....word problems.....ugh...this is the stuff of nightmares for me. LOL. :)

[LittleFredPunkinHead]

Here's what I came up with:

x=width, y=length
2x + 2y=852 where y=2x
6x=852
x=142
old area=142x284=40,328

new width=142+20=162
new length=284+40=324
new area=162x324=52,488

difference in area=52,488-40,328=12,160

[jesvet]

12160

[Adaya]

My head hurts. As soon as I saw the thread title, I knew I shouldn't have peeked in.

[Sophia]

My head hurts. As soon as I saw the thread title, I knew I shouldn't have peeked in.

No kidding. I feel like curling up in a little ball and crying.

[angelraven]

HAHA Thank you! I WAS RIGHT!

[AHammer]

oh yeah, i'm dumb. I only added 20 to the length instead of 40. oh well, I was close. ;)

[maniach]

I got 12160 too...

[phoenics]

12160 was what I got too.

What did your sister think it was?

[EJH]

My head hurts. As soon as I saw the thread title, I knew I shouldn't have peeked in.

gah, word problems...hello cold sweat. ugh.

[GoCougs]

I'm so glad everybody else got the answer that I got. Math and I definitely do not get along!

[bluberry]

12,160. That was fun! What class is this for? I want more problems! :cool:

[lindybug]

Yay, I got it right too!

This was SO MUCH FUN for me. I love this kind of math. I miss it. LOL