For this question, you have to work backwards, so if she ate a cookie, working backwards, you would have to add, not subtract or divide.
Mary had 5 cookies after she gave half away. So 5 is half of something. 5 x 2 = 10. She had 10 cookies before she gave half to her brother. Before she had 10, she ate one. So you add one to the ten.(Remember, working backwards). 10+1=11.
She had 11 cookies after she gave half. So 11 x 2 = 22. She had 22 cookies before she gave half away. She ate one before she had 22. 22+1=23. We are finished. Mary started with 23 cookies.
