320 students have food enough for 80 days. If after 20 days, 20 students leave. How many more days will the food last?
Suppose we had 25600 kg of food
or 25600/80 kg per student for 80 days,
or 1 kg per student for 1 day
so in 20 days, 320(20) kg or 6400 kgwere used
so 19200 kg are left for 300 students
time for this to last = 19200/300 = 64 days
or
do the same with a variable
let the amount of food per student be x kg
amount needed for 320 students for 80 days
= 25600x kg
in 20 days, amount used = 320(20)x or 6400x kg were used
amount left = 25600x - 6400x kg or 19200x kg
time left = 19200x/(300x) = 64 days
To find out how many more days the food will last after 20 students leave, we need to first determine the daily consumption of food per student.
We can do this by dividing the total number of days the food will last (80 days) by the number of students (320 students):
Daily consumption per student = Total number of days / Number of students
Daily consumption per student = 80 days / 320 students
Next, we can calculate the total consumption of food per day by multiplying the daily consumption per student by the total number of students:
Total consumption per day = Daily consumption per student * Number of students
Total consumption per day = (80 days / 320 students) * 320 students
Since the number of students decreases by 20 after 20 days, we need to adjust the calculation to reflect this change. We subtract the consumption of the 20 students who left from the total consumption per day:
Total consumption per day after 20 students leave = Total consumption per day - Consumption of 20 students
Finally, we can find out how many more days the food will last by dividing the remaining food by the total consumption per day after 20 students leave:
Number of days the remaining food will last after 20 students leave = Remaining food / Total consumption per day after 20 students leave
By following these steps, we can determine how many more days the food will last after 20 students leave.