lynda cut 3.2 meters of ribbon into equal size pieces. each piece was longer than 0.1 meter, but shorter than 2.o meters, with lengths in increments of 0.02 meters. How many pieces did lynda cut,and how long was each piece?

To find the number of pieces Lynda cut and the length of each piece, we need to find the total number of increments within the given range of ribbon lengths.

First, let's determine the number of increments:
The minimum length of each piece is 0.1 meters, and the maximum length allowed is 2.0 meters. The difference between the two is 2.0 - 0.1 = 1.9 meters.

Since each increment is 0.02 meters in size, we can divide the difference by the increment size to find the number of increments:
1.9 / 0.02 = 95 increments

However, we need to account for the fact that the 0.1 meter piece was already cut. So, we subtract 1 from the total number of increments:
95 - 1 = 94 increments

Now, we know there are 94 increments, but we need to determine the length of each piece. Since each increment is 0.02 meters, we can multiply the number of increments by the length of each increment to get the total length of ribbon used:
94 increments * 0.02 meters/increment = 1.88 meters

Finally, to find the length of each piece, we divide the total length of ribbon used by the number of pieces:
1.88 meters / 3.2 meters = 0.5875 meters per piece

So, Lynda cut 94 pieces, and each piece was approximately 0.59 meters long.