Algebra word problem on perimeter

Question

The kitchen rug is 7 inches longer than the width, w. The bathroom rug has a width taht is 7 inches less than the width of the kitchen rug and is 3 inches longer than the kitchen rug. The perimeter of the bathroom rug is 106 inches. Find the dimensions of each rug.

Answer 1

kitchen rug

w=width

w+7=length

 

bathroom rug

w-7=width

(w+7)+3=length

 

P=2l+2w

106=2(w+10)+2(w-7)

106=2w+20+2w-14

106=4w+6

106-6=4w

100=4w

w=100/4

w=25 inches

bathroom rug: 25-7=18 inches by 25+10=35 inches

kitchen rug: 25 inches by 25+7=32 inches