A board 20 feet long is cut into two boards with lengths in ratio of 5 to 2. To the nearest tenth of a foot, how much longer is the longer piece of the board?
S = Shorter piece
L = Longer piece
ratio of 5 to 2 means:
L = 5 S / 2
Now:
S + L = 20
S + 5 S / 2 = 20
2 S / 2 + 5 S / 2 = 20
7 S / 2 = 20
Multiply both sides by 2
7 S = 40
S = 40 / 7
L = 5 S / 2
L = ( 5 ∙ 40 / 7 ) / 2 = ( 200 / 7 ) / 2 = 200 / 7 ∙ 2 = 200 / 14 = 14.2857142
L = 14.3 ft
to the nearest tenth