Math helpv

Question

It cost $116.45 frame a painting with a flat aluminum strip. This is caulculated at $1.37 per foot for materials and labor. Find the dimensions of the painting of its length is 3 feet less than four times it's width. The length of the painting is____feet

Answer 1

Length is 3 less than 4 times the width:

1)  L = 4w - 3

 

(Cost per foot)(perimeter in feet) = 116.45

2)  1.37(2L + 2w) = 116.45 

 

We have two equations.  In equation 2 replace

L with 4w-3 and solve for w

 

1.37(2(4w-3)+ 2w) = 116.45

1.37(8w-6+2w) = 116.45

1.37(10w-6) = 116.45

10w-6 = 116.45/1.37

10w-6 = 85

10w = 91

w = 9.1 ft

 

L = 4w-3 = 4(9.1)-3 = 33.4 ft

 

Answer 2

85 feet of frame is used (116.45 / 1.37)

85 = 2(w + 4w - 3)

42.5 = 5w - 3

45.5 = 5w

9.1 = w

 

What is the length?