Ashelter has enough food to feed an average of 80 hungry people a day for 14 days. if an average of 32 people are at the shelter each day, how long will the food last?

Explanation

The capacity of the shelter is a constant. It is 80 people × 14 days.

That is an inverse relation: the product of the number of people and the number of days will be always the same.

As the number of people decreases the number of days that the food lasts increases, in a proportion such that the product of the days and the number of people is the same.

Thus, for 32 people the number of days the food lasts is x, such that:

Solving for x:

The food will last 35 days.

35 days

Step-by-step explanation:

Given: A shelter has enough food to feed an average of 80 hungry people a day for 14 days.

Let y be the number of days if  32 people are at the shelter .

The number of hungry people and number of days are in inverse proportion

Therefore,

Therefore, if an average of 32 people are at the shelter each day, the food will last for 35 days.