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?

Answer 1

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