Lumber word question

Question

Woodsmith magazine gave instructions on how to build a pine cupboard. Lumber will be needed for two shelves 11 1/4 inches long, two base sides 12 1/2 inches long, and two door stiles 28 1/8 inches long. Your lumber comes in 6 foot lengths.
a. How many feet of lumber will you need?

 

I've tried solving it 3 different times and I don't know what I'm doing wrong.

Answer 1

2 x (11 and 1/4) + 2 x (12 and 1/2) + 2 x (28 and 1/8) =

 

2 x 45/4  + 2 x 25/2 + 2 x 225/8 =

 

45/2 + 25 + 225/4 =

 

90/4 + 100/4 + 225/4 =

 

415/4 =

 

103 and 3/4 inches of lumber is needed

 

6 feet = 6 feet x 12 inches per foot = 72 inches

 

103 and 3/4 divided by 72 =

 

415/4 divided by 72 =

 

415 / 4 x 1/72  <--- remember when dividing fractions, KFC: keep, flip, change

 

415/ 288 =

 

1 and 127/288

 

Now,

288 = 2 x 144 = 2 x 12 x 12 = 2 x 2 x 2 x 3 x 2 x 2 x3.

So the only factors of 288 and 2 and 3, and neither one

divides 127 evenly. So the fraction is reduced to lowest terms.