a paper company word problem

Question

A paper company makes rectangular pieces of cardboard for packing computers. The sheets of cardboard are to have an area of 130 square inches, and the length of a sheet is to be 77 inches more than three fifth its width. Determine the length and width of the cardboard to be manufactured.

 

Answer 1

Hi J;

 

L = 3w/5 + 77

A = LW = 130

 

w(3w/5 + 77) = 130

 

3w²/5 + 77w = 130

 

3w² + 385w = 650

 

3w² + 385w - 650 = 0

 

Now use quadratic equation to solve for w

 

w = [-385 ±√(385² - 4(3)(-650))]/2(3)

w = [-385 ±√156025]/6

w = (-385 ± 395)/6

Since the width will be positive we can disregard the (-385-395)/6

 

w = 10/6 = 5/3 inches

 

L = (3/5)(5/3) + 77 = 78 inches

 

The cardboard is 78 inches by 1 2/3 inches

 

Check LW = 78(5/3) = 130 in²

Answer 2

130 = (w)(3/5w+77)

 

130 = 3/5w^2 + 77w

 

650 = 3w^2 + 385w

 

0 = 3w^2 + 385w  - 650

 

0 = ( 3w   -       5       )( w  + 130          )

 

w+130 = 0 results in a negative width

 

width is 5/3

 

length is 3/5*5/3 + 77 = 78