Final answer:
To find the greatest number of identical sets with no items left over, one must calculate the greatest common divisor of the number of tee shirts and buttons. For 22 tee shirts and 50 buttons, the greatest common divisor is 2, yielding 2 sets with 11 tee shirts and 25 buttons each.
Step-by-step explanation:
The student question asks how to create the greatest number of identical sets from a collection of 22 tee shirts and 50 buttons with no items left over. This problem can be solved by finding the greatest common divisor (GCD) of the two numbers, which is the largest number that divides both 22 and 50 without leaving a remainder. The GCD of 22 and 50 is 2. Therefore, the greatest number of identical sets that Ellie can create is 2, with each set containing 11 tee shirts and 25 buttons.