Final answer:
The seamstress used a total of 170 buttons for her mending; 120 from the first box and an additional 50 from the second box.
Step-by-step explanation:
The problem involves calculating the total number of buttons the seamstress used for her mending. First, we find out how many buttons she had left in the first box. She had 3/5 of 200 buttons, which equals 120 buttons. For the mending, she used these 120 buttons plus 1/4 of another box of 200 buttons, which is 50 buttons (200 * 1/4). Therefore, the total number of buttons used is 120 buttons from the first box plus 50 buttons from the second box, which equals 170 buttons in total.