twelve students bought food for a ten -day camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by there more students but do not buy more food. how long will the food last if the original daily share for each student is unchanged ?

Initially, twelve students had food for a 10-day camping trip, with each student receiving an equal daily share. Let’s break down the problem:

1. **Total Amount of Food:** 
   Since the food was supposed to last 12 students for 10 days, we can represent the total amount of food as:
   \[
   \text{Total food} = 12 \text{ students} \times 10 \text{ days} = 120 \text{ student-days}
   \]
   This means the food supply is enough for 120 "student-days" if each student maintains their share.

2. **New Group Size:** 
   When three more students join, there are now:
   \[
   12 + 3 = 15 \text{ students}
   \]

3. **Duration of Food Supply for 15 Students:** 
   To find out how many days (\(d\)) the food will last for 15 students while maintaining the same daily share, we divide the total student-days by the number of students:
   \[
   d = \frac{120 \text{ student-days}}{15 \text{ students}} = 8 \text{ days}
   \]

So, the food will last for **8 days** with 15 students if each student continues to receive the same daily share as initially planned.

Would you like a breakdown of this solution, or do you have any questions?

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### Related Questions

1. What if the number of extra students was five instead of three?
2. How many days would the food last if they decide to reduce each student's daily share to extend the trip?
3. How much food would they need to bring if they wanted the food to last 10 days with 15 students?
4. If only 10 students went on the trip, how many days would the food last?
5. What happens to the daily share per student if they bought food for 15 days instead?

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### Tip  
For problems involving "per person" resources, consider calculating in terms of "person-days" or "student-days" to make adjustments easier when group sizes change.

Twelve students bought food for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by three more students but do not buy more food. How long will the food last if the original daily share for each student is unchanged?

Discover how to calculate the duration of a food supply when three additional students join a group of twelve. This problem covers basic arithmetic and proportionality concepts, showing that the food will last for 8 days if each student keeps their initial share. Ideal for students in Grades 6-8.

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