SOLUTION: PI need your help with this problem I am not sure how you would set it up. A recreation department plans to build a rectangular playground enclosed by 1000 meters of fence. If the

Algebra ->  Linear-equations -> SOLUTION: PI need your help with this problem I am not sure how you would set it up. A recreation department plans to build a rectangular playground enclosed by 1000 meters of fence. If the       Log On


   

Question 233734: PI need your help with this problem I am not sure how you would set it up. A recreation department plans to build a rectangular playground enclosed by 1000 meters of fence. If the length of the playground is 4 meters less than 3 times the width find the length and width of the playground. I think the best way to set it up is 1000=(2l-4+2wcubed)but not sure please help me.
Found 2 solutions by rfer, Theo:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
P=2w+2L
1000=2w+2(3w-4)
1000 2w+6w-8
1008=8w
w=126 m
3w-4=374 m

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A recreation department plans to build a rectangular playground enclosed by 1000 meters of fence. If the length of the playground is 4 meters less than 3 times the width find the length and width of the playground.
L = length of the playground
W = width of the playground.
Perimeter of the playground is 1000 meters.

P = Perimeter of the playground.

P = 2L + 2W

1000 = 2L + 2W

Length of the playground is 4 meters less than 3 times the width.

L = 3*W - 4

Replace L with 3*W-4 to get:

1000 = 2L + 2W becomes:

1000 = 2 * (3W-4) + 2W which becomes:

1000 = 6W - 8 + 2W which becomes:

1000 = 8W - 8

Add 8 to both sides to get:

1008 = 8W

Divide both sides by 8 to get:

W = 126

If W = 126, then:

L = 3*W - 4 = 374

P = 1000 = 2L + 2W = 2*374 + 2*126 = 1000

L = 3*W - 4 = 3*126 - 4 = 374 is ok.

Perimeter equals 1000.
L = 3W - 4

Everything looks good so the answer is:

L = 374
W = 126