a 36 inch stick is broken into 2 pices if one piece is 8 inches longer than the other how long is the other piece

Question

36 inch stick broken into 2 pieces

if one piece is 8 inches longer than the other

how long is the other piece

 

Answer 1

There are 2 ways to attack this:

•      Since the stick is 36 inches long, if broken exactly in the middle, each piece would be 18 inches. The problem tells us one piece must be 8 inches longer than the other, so imagine cutting 4 inches off one of the halves, and attaching it to the other. This leaves a piece that is 14 inches  (18-4) and another that is 22 inches (18+4). The difference in lengths is 8 (22-14)
• Second approach: The 2 pieces will be called x and y. We know that x+y=36, the total length of original stick, AND that x+8=y (or y+8=x, it makes no difference ), because one piece is 8 inches longer than the other. Substituting for y in  the first equation we get:       x+y=36

                          x+(x+8)=36

 

                          2x+8=36

 

                         2x=36-8

 

                         2x=28

 

                         x=14       Since y=x+8, 

 

                                                   y=14+8

 

                                                   y=22

 

Answer 2

S = Shorter piece

L = Longer piece

 

S + L = 36

L = S + 8

 

S + S + 8 = 36

2S + 8 = 36

2S = 28

S = 14

 

The shorter piece is 14" and the longer piece is 22".