Final answer:
The pair of quantities that is least likely to be directly proportional is total cost and the number of hats purchased.
Step-by-step explanation:
In this question, we are asked to identify the pair of quantities that is LEAST likely to be directly proportional.
1. Hours worked and money earned: These two quantities are directly proportional. As the number of hours worked increases, the amount of money earned also increases.
2. Distance and time when speed is constant: These two quantities are directly proportional. If the speed is constant, the distance traveled is directly proportional to the time taken.
3. Area and side length of a square: These two quantities are directly proportional. As the side length of a square increases, the area also increases.
4. Total cost and the number of hats purchased: These two quantities are NOT likely to be directly proportional. The total cost may depend on factors other than just the number of hats purchased, such as discounts or shipping fees.
Therefore, the pair of quantities that is LEAST likely to be directly proportional is 4. Total cost and the number of hats purchased.