From 304 marbles, ignoring the constraint of having at least one bag with 11 marbles, what is the maximum number of bags that can be formed using only 9-marble bags?

From 304 marbles, ignoring the constraint of having at least one bag with 11 marbles, what is the maximum number of bags that can be formed using only 9-marble bags?

• A. 29
• B. 33
• C. 32
• D. 34

Answer: (C)

The key idea is to maximize full 9-marrow bags from a total of 304 marbles, so you take as many complete groups of 9 as possible. Divide 304 by 9: 9 × 33 = 297, and 9 × 34 = 306 which is too many. That means you can form 33 bags using 297 marbles, leaving 7 marbles unused. You can’t reach 34 bags because you’d need 306 marbles. So the maximum number of bags is 33.

The key idea is to maximize full 9-marrow bags from a total of 304 marbles, so you take as many complete groups of 9 as possible. Divide 304 by 9: 9 × 33 = 297, and 9 × 34 = 306 which is too many. That means you can form 33 bags using 297 marbles, leaving 7 marbles unused. You can’t reach 34 bags because you’d need 306 marbles. So the maximum number of bags is 33.