A200 centimeter-long wire is cut into three pieces. the second piece is 3 times as long as the first. the third piece is 2 times as long as the second. how long is each piece?

Let x be the length of the first piece, y be the length of the second piece and z be the length of the 3rd piece. We just need to figure out how these lengths (x,y,z) relate to the total length and each other as follows:

x + y + z = 200 since the sum of the lengths equals the total length of the wire

y = 3x since piece two is 3 times longer than piece one
z = 2y = (2)(3)(x) = 6x since piece three is 2 times longer than piece two

Now we have (x,y,z) in terms of x alone, so we can substitute into the first equation:

x + 3x + 6x = 10x = 200 which means x = 20.

Then, substitute this value into all the other equations.

y = 3(20) = 60
z = 6(20) = 120

This can be checked by summing them up like this: 20 + 60 + 120 = 200.