Story problem in algebra

Question

A contractor is installing carpet in a new house. The rectangular living room has an area of 96 square feet, and the length is twelve feet less than three times the width of the room. What are the dimensions of the room?

Answer 1

Area = length*width

 

Lw = 96

L = 3w - 12

 

w(3w-12) = 96

3w² - 12w - 96 = 0

3(w² - 4w - 32) = 0

w² - 4w - 32 = 0

(w-8)(w+4)  = 0

w = 8 or -4

 

Discount the negative answer, the 

width is 8 ft

 

L = 3w - 12 = 12 ft

 

The dimensions are 12 ft by 8 ft