Simple three rule is a practical process for solving problems involving four values of which we know three of them. We must therefore determine a value from the three already known.

## Steps used in a simple three rule

**1º)** Construct a table by grouping the quantities of the same species into columns and keeping in line with the quantities of different species in correspondence.

**2º)** Identify whether the quantities are directly or inversely proportional.

**3º)** Assemble the ratio and solve the equation.

## Examples

1) With a solar absorption area of 1.2m^{2}, a solar-powered motorboat can produce 400 watts per hour of power. Increasing this area to 1.5m^{2}, what will be the energy produced?

*Solution:* setting up the table:

Area (m^{2}) | Energy (Wh) |

1,2 | 400 |

1,5 | x |

*Relationship Type Identification:*

Initially we put a down arrow on the column containing x (2nd column). Notice that, **increasing** absorption area, solar energy **increases**. As the words correspond (increasing - increasing), we can say that the magnitudes are **directly proportional**.

So we put another arrow in the same direction (down) in the 1st column. *Riding the ratio and solving the equation we have*:

Therefore, the energy produced will be **500 watts per hour**.

2) A train, moving at an average speed of 400 km / h, makes a certain journey in 3 hours. How long would that same route be if the speed used was 480km / h?

*Solution:* setting up the table:

Speed (Km / h) | Time (h) |

400 | 3 |

480 | x |

*Relationship Type Identification:*

Initially we put a down arrow on the column containing x (2nd column). Notice that, **increasing** the speed, the travel time **decreases**. Since the words are contrary (increasing - decreasing), we can say that the quantities are **inversely proportional**.

So we put another arrow upwards in the 1st column. *Riding the ratio and solving the equation we have*:

Therefore, the time of this route would be **2.5 hours or 2 hours and 30 minutes**.

3) Bianca bought 3 t-shirts and paid $ 120.00. How much would she pay if she bought 5 shirts of the same type and price?

*Solution:* setting up the table:

T-Shirts | Price (R $) |

3 | 120 |

5 | x |

Notice that, **increasing** the number of t-shirts, the price **increases**. As the words correspond (increasing - increasing), we can say that the magnitudes are **directly proportional**.

*Riding the ratio and solving the equation we have*:

Soon, Bianca would pay **$ 200** by 5 shirts.

4) A team of workers, working 8 hours a day, performed a certain work in 20 days. If the number of hours of service is reduced to 5 hours per day, when will this team do the same work?

*Solution:* setting up the table:

Hours per day | Deadline (days) |

8 | 20 |

5 | x |

Notice that, **decreasing** the number of hours worked per day, the deadline to finish **increases**. Since the words are contrary (decreasing - increasing), we can say that the quantities are **inversely proportional**.

*Riding the ratio and solving the equation we have*: