Shirts on Sale

TOPS, Inc. has a sale table with 49 shirts. Every shirt is plaid, wool, or has a button-down collar. There are twice as many plaid shirts as shirts with button-down collars. Twenty-one of the plaid shirts are not wool. There are 12 shirts with button-down collars. There is only one wool plaid shirt with a button-down collar. Half of all of the shirts with button-down collars are wool. Every plaid shirt with button-down collar is wool. How many wool shirts are not plaid and do not have a button-down collar?

Reference from Greenes, Carol, Linda Schulman, Rika Spungin, Suzanne Chapin, Carol Findell. Mathletics: Gold Metal Problems. Providence RI: Janson Publications Inc., 1990.