29. Rule of three simple and compound

The rule of three is one of the most used mathematical tools in solving problems involving the relationship between three or more quantities. It can be classified into two types: the simple rule of three and the compound rule of three. Both are essential topics for the Enem test and, therefore, deserve special attention during the preparation for the exam.

Rule of three simple

The simple rule of three is used when we have two magnitudes directly or inversely proportional. We say that two magnitudes are directly proportional when the increase of one implies the increase of the other in the same proportion. On the other hand, two magnitudes are inversely proportional when the increase of one implies the decrease of the other.

To solve a problem using the simple rule of three, we first identify whether the quantities are directly or inversely proportional. Afterwards, we set up a table with the values ​​of the quantities and, finally, we solved the proportion to find the unknown value.

For example, if a person can type 200 words in 5 minutes, how many words can he type in 15 minutes? In this case, we have two directly proportional quantities (time and number of words). Setting up the table and solving the proportion, we find that the person will be able to type 600 words in 15 minutes.

Rule of three compound

The compound rule of three is used when we have three or more quantities that are related. As with the simple rule of three, quantities can be directly or inversely proportional.

Solving a problem using the compound three rule is a bit more complex. First, we identify the quantities and their proportionality relationships. Afterwards, we set up a table with the values ​​of the magnitudes. Then we multiply the values ​​of the directly proportional quantities by the unknown value and the values ​​of the inversely proportional quantities by the inverse of the unknown value. Finally, we solve the equation to find the unknown value.

For example, if a factory produces 1000 parts in 5 days with 10 workers, how many parts will be produced in 10 days with 20 workers? In this case, we have three magnitudes (number of parts, number of days and number of workers) that are all directly proportional. Setting up the table and solving the equation, we find that 4000 pieces will be produced in 10 days with 20 workers.

In summary, the rule of three is a simple and effective method for solving problems involving the relationship between quantities. Whether using the simple rule of three or the compound rule of three, the important thing is to correctly identify the magnitudes and their proportionality relationships. With practice and dedication, you will be able to solve any rule of three problem that appears on the Enem test.

Studying math for the ENEM can seem challenging, but with the right strategies and a good understanding of fundamental concepts such as the rule of three, you will be able to solve problems with confidence and accuracy. Remember that practice is the key to success, so be sure to tackle plenty of exercises and questions from past exams. Good luck!

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