Awooden board 100 centimeters long is cut into two pieces. one piece is 16 centimeters longer than the other. what are the lengths of the two pieces?

x = the length of one piece

y = the length of the other piece

the total length is 100 cm this means 

x + y = 100

one piece is 16 inches longer than the other

first we need to convert inches to cm: 

1 in = 2.54 cm

16 in = 2.54*16 = 40.64

now we can write

x = y + 40.64

by solving the system of equations

x + y = 100

x = y + 40.64

we find

x = 70.32 cm

y = 29.68 cm

the lengths of the two pieces are 70.32 cm and 29.68 cm.