In your quilt shop, you make and sell quilts. you like to have a total of 26 yards of royal blue fabric in stock at the beginning of each month. today your inventory includes 4 pieces of this fabric that are each 22 1/2 inches long and 3 pieces that are each 33 inches long. you must purchase this fabric in 3 yard long pieces. to replenish your stock, how many pieces do you need to buy?

7 pieces

Step-by-step explanation:

Stock that must be available at the beginning of each month = 26 yards

Since,

1 yard = 36 inches

26 yards = 26 x 36 = 936 inches

This means 936 inches of fabric must be available at beginning of each month.

Current Inventory:

4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics =  4 x 22.5 = 90 inches

3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches

Therefore, the total length of current inventory = 90 + 99 = 189 inches.

Length of fabric needed more:

Length of fabric that must be bought more = 936 - 189 = 747 inches

It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.

So,  I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.

Therefore, the number of pieces that I need to buy =

Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.