SOLUTION: 72 persons have enough food for 7 days but after one day they decided to finish the food in 3 remaining days. For it they invited more persons. how many persons did they invite?

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Question 808195: 72 persons have enough food for 7 days but after one day they decided to finish the food in 3 remaining days. For it they invited more persons. how many persons did they invite?
Found 3 solutions by richwmiller, josgarithmetic, MathTherapy:
Answer by richwmiller(17219)   (Show Source):
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72*7=504 person days of food
after one they have used 72 person days
504-72=432 person days remaining after one day
432/(72+x)=3
x=72 more invited
which makes sense since now they have 6 days for 72

Answer by josgarithmetic(39614)   (Show Source):
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This is a job-task completion, uniform rates problem. The JOB is "consume the allotment of food".

Very obviously, we want the one-person food-consumption rate.
72 persons need 7 days;
1 person needs 7*72 days.
The one-person rate is jobs per day.

Food consumption went this way:
1 day for 72 persons, and then 3 days with 72+n persons, to consume the 1 allotment of food. That 1 allotment is the 1 job.
Rate*Days=Job
Here, Job is 1. We have the sum of two job quantities.

You should find that equation easily enough to solve for n, the count of additional persons who were invited and shared in consuming the food. The most important part of the solution was the process to form that highlighted equation, and the discussion about it.

Answer by MathTherapy(10549)   (Show Source):
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72 persons have enough food for 7 days but after one day they decided to finish the food in 3 remaining days. For it they invited more persons. how many persons did they invite?

invitees