120 quilts were entered into a quilt show. (Traditionally, all quilts were hand stitched but now many are stitched on machines. Appliques are additional pieces of cloth that are sewn on top of the quilt.) In this show, 86 were machine stitched. 44 had appliques applied. 24 were both machine stitched and had appliques

And your question is??

To find the number of quilts that were either machine stitched or had appliques applied, we can use the principle of inclusion-exclusion.

First, we add the number of quilts that were machine stitched to the number of quilts that had appliques applied. Therefore, 86 + 44 = 130 quilts were either machine stitched or had appliques applied.

However, this count includes the quilts that were both machine stitched and had appliques applied. To correct this, we need to subtract the number of quilts that fall into this category. Therefore, we subtract 24 from the previous count of 130.

130 - 24 = 106 quilts were either machine stitched or had appliques applied.

Now, to find the number of quilts that were neither machine stitched nor had appliques applied, we subtract this count from the total number of quilts:

120 - 106 = 14 quilts were neither machine stitched nor had appliques applied.

Therefore, there were 106 quilts that were either machine stitched or had appliques applied, and 14 quilts that were neither.