Word Problem; Perimeters of two rugs

faith14

New member
Joined
Nov 24, 2007
Messages
7
I'm having problems with another world problem. A kitchen rug is 7 inches longer than its width. A bathroom rug has a width of 7 inches less that the kitchen rug but 3 inches longer. The perimeter of that bathroom rug is 106 inches. Find the dimensions of both rugs. I can't figure out if this is supposed to be two separate problems or what.

The variables for the kitchen rug I think would be 2(x) + 2(x + 7) for the width and length. Should the equation for the bathroom rug be 2(x - 7) + 3 = 106? I don't know what the next step is or if I'm messing this one up and that's the reason I'm stuck. Should the equation also contain the kitchen rug formula.

Thanks!
 

jwpaine

Full Member
Joined
Mar 10, 2007
Messages
723
Re: Word Problem; Perimeter

faith14 said:
I'm having problems with another world problem. A kitchen rug is 7 inches longer than its width. A bathroom rug has a width of 7 inches less that the kitchen rug but 3 inches longer. The perimeter of that bathroom rug is 106 inches. Find the dimensions of both rugs. I can't figure out if this is supposed to be two separate problems or what.
Let L = length; W = width:

Kitchen rug:
L =(W + 7)
W = (L - 7)

Bathroom rug:
W = (L - 14)
L = (W + 10)

perimeter (bathroom rug) = 2W + 2L = 106

2(L - 14) + 2(W + 10) = 106
2L - 28 + 2W + 20 = 106
2L + 2W -8 = 106
L + W - 4 = 53
L + W = 57

W = 57 - L <--- substitute this into either the kitchen or the bathroom equations to generate W and L

Bathroom:
57 - L = L - 14
71 = 2L
==> L = 35.5

W = 35.5 - 7
==> W = 28.5

Now use those two values and plug them back into each bathroom and kitchen L and W formula, to find the dimensions of each.
 

faith14

New member
Joined
Nov 24, 2007
Messages
7
Re: Word Problem; Perimeter

Thanks again!
 
Top