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?
My work:
44= 28+17+22-12-10-5+x
X=4
Your work is correct! To find the number of bolts that are broadcloth floral prints with a blue background, we can use the principle of inclusion-exclusion.
Let's break down the equation step by step:
Total number of bolts on the clearance table (44) = Number of broadcloth bolts (28) + Number of floral prints (17) + Number of bolts with a blue background (22) - Number of bolts that are both floral prints and broadcloth (12) - Number of bolts that are both broadcloth and have a blue background (10) - Number of bolts that are both floral prints and have a blue background (5) + Number of bolts that are broadcloth floral prints with a blue background (x)
Now let's solve for x:
44 = 28 + 17 + 22 - 12 - 10 - 5 + x
Simplifying the equation:
44 = 40 + x
Subtracting 40 from both sides of the equation:
44 - 40 = x
4 = x
So, your answer of 4 is correct. There are 4 bolts that are broadcloth floral prints with a blue background.