For those interested, there is a trick to this. You successively add the first several items until the amount first exceeds 43.94. This occurs after summing up the first twelve items, with the sum being 46.81. The items are over the limit by 2.87.

You wish to decrease your spending by $2.87, so you check if there are any items you have not chosen that cost exactly $2.87 less than an item you have chosen. A smart fifth-grader would quickly find that the car ($5.18) can be replaced by Jacks ($2.31). This concludes the problem-solving process.

This question was intended for fourth- and fifth-graders (https://www.insidemathematics.org/sites/default/files/materi...). Put yourself in the shoe of a smart fifth-grader who knows nothing about NP-completeness or knapsack problems. This problem is given to you, and you know it as solvable. This problem would look intimidating, but a good student would look for patterns, and the best way to start looking would be to sum the first few items (who knows, maybe the first items would sum up to exactly $43.94). After summing up to 46.81, a good student would "naturally" stop adding new items and ask himself "what can be done now?" All that he needs is now a mental "click".

Essentially, this problem tests students' intuition. It tests whether students can remain unintimidated in the face of difficult-looking questions. They need to start adding, and they need to have that one insight of replacing one of the items. Insights like these are extremely common and rewarding for young math learners.

I won't be surprised if many fifth-graders can solve the problem in five minutes.