Farmer has enough food to feed his family for 10 Days. If 3 out of 8 members leave the house, then for how many days will the food last?

Farmer has enough food to feed his family for 10 Days. If 3 out of 8 members leave the house, then for how many days will the food last?

To determine how long the food will last if 3 out of 8 members leave the house, you can follow these steps.

The food can last for 10 days for 8 members

When 3 members leave, the number of remaining members becomes 5

The number of days the food lasts is inversely proportional to the number of members. Fewer members mean the food lasts longer.

We use the formula for proportionality

x1/x2 = y2/y1

Where

x1 = Initial number of members = 8

x2 = New number of members = 5

y1 = Initial number of days = 10

y2 = New number of days

Substitute the values into the proportion

8/5 = y2/10

Therefore y2 = 16

Hence, the food will last for 16 days.

Inverse Proportionality

In mathematics, understanding proportional relationships is essential for solving problems involving quantities that change in relation to each other. One common type of proportional relationship involves inverse proportionality, where as one quantity increases, the other decreases, and vice versa.

When dealing with inverse proportionality, such as determining how long a supply of food will last for a group of people, the key concept is that fewer people consuming the same amount of food will make it last longer. This principle applies because the rate at which the food is consumed decreases as the number of consumers decreases.

To establish how long a supply of food will last for a different number of people, mathematicians use a formula derived from the concept of inverse proportionality

x1/x2 = y2/y1

Here, x1 and x2 represent the initial and new quantities of a variable (such as the number of people), respectively.

Similarly, y1 and y2 represent the initial and new quantities of another variable (such as the number of days the food will last), respectively.

By applying this formula, you can calculate how changes in one variable affect another in an inverse proportionate manner.