120 -inch length of ribbon is to be cut into three pieces. the longest piece is to be 40 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. find the length of each piece of ribbon.

1. Let
Shortest piece = x
Longest piece = y
Third piece = z

2.
Shortest piece = x
Longest piece = 40 + x
Third piece = (40 + x)/2 OR 20 + 0.5x

3. Add all the expressions since you know that the total of all the pieces is 120 inches
40 + x + 20 + 0.5x + x = 120.

4. Add the whole numbers first, then add the variables.
40+20=60
x+0.5=2.5x
60+2.5x=120

5. To get rid of the 60, do the opposite of addition which is subtraction and subtract 60 from both sides.
2.5x=120-60
2.5x=60

6. Do the same but rather than addition, do the opposite of multiplying which is dividing, on both sides.
x=60/2.5
x=24

7.
Shortest piece = 64-40=24 inches
Longest piece = 24+40=64
Third piece = 64/2=32