How to Calculate Wheat Consumption: A Comprehensive Guide

Understanding the requirement of wheat for a certain number of people over a specific time period is an essential skill in resource management and planning. This article aims to illustrate the mathematical approach to solving such problems using various methods, including ratio and proportion, linear equations, and efficiency calculations.

Ration and Proportion Method

Let's consider the problem: If 42 persons consume 144 kg of wheat in 15 days, how many days will 30 persons consume 48 kg of wheat? We can simplify the problem using the concept of ratio and proportion.

Given:

42 people consume 144 kg in 15 days. 30 people consume 48 kg in x days.

Setting up the proportion:

[ frac{144 text{ kg}}{42 text{ people} times 15 text{ days}} frac{48 text{ kg}}{30 text{ people} times x text{ days}} ]

Simplifying the left side:

[ frac{144}{42 times 15} ]

Solving for x:

[ frac{144}{42 times 15} frac{48}{30 times x} ]

Simplifying further:

[ frac{144}{630} frac{48}{3} ]

[ frac{24}{105} frac{48}{3} ]

[ frac{24}{105} frac{48}{2x times 30} ]

[ frac{24}{7} frac{48}{2x} ]

[ frac{24}{7} frac{24}{x} ]

[ x 7 text{ days} ]

Hence, 30 people will consume 48 kg of wheat in 7 days.

Efficiency and Linear Equations

An alternative approach is to consider the efficiency of individual consumption. 72 people consume 144 kg in 7 days, so the daily consumption per person is:

[ text{P} frac{144}{72 times 7} frac{2}{7} text{ kg/day per person} ]

For 30 people, the daily consumption would be:

[ 30 text{ people} times frac{2}{7} text{ kg/day per person} times X text{ days} 45 text{ kg} ]

Solving for X:

[ X frac{45 times 7}{30 times 2} frac{315}{60} frac{21}{4} 5.25 text{ days} ]

Direct Proportion Method

Another method involves direct proportion. Given 72 people consume 144 kg in 7 days, we can calculate the time required for 30 people to consume 45 kg.

[ 72 text{ people} times 7 text{ days} 504 text{ person-days} ]

For 30 people to consume 45 kg:

[ 30 text{ people} times X text{ days} 157.5 text{ person-days} ]

[ X frac{157.5}{30} 5.25 text{ days} ]

Hence, 30 people will consume 45 kg of wheat in 5.25 days.