Final answer:
To find out how long a 100kg bag of beans will last for 16 students, we set up an inverse proportion where 40 students consume the beans in 6 weeks. Solving the proportion (40 students * 6 weeks) = (16 students * x weeks) reveals that the bag will last for 15 weeks for the 16 students.
Step-by-step explanation:
If 40 students consume a 100kg bag of beans in 6 weeks, we can determine how long the bag will last for a smaller number of students using a simple proportion. Since the amount of beans consumed is inversely proportional to the number of students, we can set up a ratio where 40 students is to 6 weeks as 16 students is to x weeks:
Step-by-Step Solution:
First, write the proportion: 40 students / 6 weeks = 16 students / x weeks.
Solve for x: (40 students * 6 weeks) = (16 students * x weeks).
Calculate the number of weeks: x = (40 * 6) / 16.
Divide to find the answer: x = 240 / 16.
Thus, x = 15 weeks.
Therefore, a 100kg bag of beans will last 15 weeks for 16 students.