Final answer:
The board is to be cut into pieces of 20 cm and 89 cm, where the longer piece is 9 cm more than 4 times the length of the shorter piece.
Step-by-step explanation:
A 109-cm long board is to be cut into two pieces so that one part is 9 cm more than 4 times as long as the shorter part. Let's denote the length of the shorter part as x cm. Then, the longer part would be 4x + 9 cm. Since the sum of the two parts equals the total length of the board, we can formulate an equation:
x + (4x + 9) = 109
Now, solving for x, we get:
5x + 9 = 109
5x = 109 - 9
5x = 100
x = 100 / 5
x = 20
So the shorter part of the board is 20 cm. The length of the longer part is:
4x + 9 = 4(20) + 9 = 80 + 9 = 89 cm
Therefore, the two pieces of the board measure 20 cm and 89 cm, respectively.