a cable 20 ft long is cut into two pieces the length of one piece is two-third of the legnth of the other piece.

Question

Fine the length of the shorter piece.

Answer 1

Algebra approach: Let S be the shorter length, and L be the longer length. We know two equations for S and L:

 

S = (2/3)*L

 

S + L = 20 ft

 

We want to find S, so we eliminate L.  From the first equation, solve for L and you get

 

L = (3/2)*S

 

Now replace L by S in the second equation:

 

S + (3/2)*S = 20 ft

 

Solve for S:

 

(1 + 3/2)*S = (5/2)*S = 20 ft

 

S = (2/5)*20 ft

 

S = 8 ft <---Answer.

 

Check: 8 ft is 2/3 of 12 ft, so L = 12 ft.  S + L = 8 ft + 12 ft = 20 ft. The answer checks out.

Answer 2

Let x = the length of the longer piece.  The length of the shorter piece is (2/3)x.

 

x + (2/3)x = 20 feet

 

(3/3)x + (2/3)x = 20

 

(5/3)x = 20

 

x = 20*(3/5)

 

x = 12 feet    This is the longer piece.  The shorter piece is (2/3)x = (2/3)(12) = 8 feet