A fabric store has 44 bolts of fabric on its clearance table. Of these bolts 28 are broadcloth, 17 floral prints, 22 have a blue background, 12 floral prints on broadcloth, 10 arare broadcloth with a blue background, and 5 are floral prints with blue background. If all but 2 of the clearance fabrics fitfit a least one of these categories, how many of the bolts are broadcloth floral prints with a blue background. I get 4 is this correct?

Question

My work:
44= 28+17+22-12-10-5+x
X=4

Answer 1

You ignored that fact that "If all but 2 of the clearance fabrics fitfit a least one of these categories"
That tells me that of the 44 bolts there were 2 that did not fit any of the given properties, so we only have 42

so change your equation to:
42 = 28+17+22-12-10-5+x
x = 2

filling in your Venn diagrams will show that there are 8 with broadcloth and blue background