# Simple rule of three

If there is any **knowledge** which is **essential** for the **human** being , without a doubt it is basic mathematics. However, these are tedious to **learn** or **enlighten** , they allow almost a **basic** part of **life** , from taking **accounts** in **supermarkets** to know how much to spend, to forming bases for subjects such as **physics** , **statistics** , among others. For example, in the case of **the simple rule of three, it** allows to **isolate** an **unknown ****variable** through the other three accompanying compounds.

## What is the simple rule of three?

The **simple rule of three** is a mathematical operation used to **solve problems** of **direct** and ** inverse ****proportionality** . To make a simple rule of three, 3 pieces of information **are needed** , two of which are **proportional to** each other. With these data we can easily find out what is the value of the **fourth term** of proportionality.

- What does it consist of
- What is the simple rule of three for?
- Direct simple rule of three
- Inverse simple rule of three
- Other examples

## What does it consist of

A **compound rule of three is used** when there are **two proportional magnitudes involved** and a **third magnitude** that allows quickly and simply to solve the unknown.

## What is the simple rule of three for?

**The simple rule of three** gives us the **solution** to **solve analysis problems** where there are three **known quantities** and one whose value is unknown.

## Direct simple rule of three

When talking about the ** direct simple rule of three it** is the method used when the problem presented two quantities **directly in proportion. **It can be said that two quantities are directly in proportion when, by multiplying or dividing one of them by a number, the other is multiplied or divided correspondingly by the same number.

To solve a direct simple rule of three, you just have to follow the following formula:

- A / C = B / X establishing it in the formula to solve for X would be X = B x C / A

This is best understood by solving an example

It is known that for every **100 grams of sugar you have to add 10 grams of salt. **You can **enlarge** or **reduce** the **amounts** , but if you want to follow the recipe, these amounts should keep a **proportion** . That is why if you add **double the sugar** of what the recipe says, you will have to add **double the salt** and therefore if you add **triple the sugar** of what the recipe says, you would also have to add **three times more amount of salt.**

This is understood as that if the amount of sugar increases in the same way, the amount of salt must grow in proportion. In this problem, **sugar and salt are directly proportional amounts** .

## Inverse simple rule of three

When talking about the ** direct simple rule of three, it** is the method used when the problem presents two magnitudes **inversely in proportion. **It can be said that two **quantities are inversely proportional ** when **multiplying one of them by a number** , the other is divided by the same, and inversely.

To solve a **simple inverse** rule of three we have to follow the following formula:

- A / C = B / X establishing it in
**the formula to solve for****X would be**X = A x B / C

This is best understood by solving an example

In a gas station **there are** only **two pumping towers** , so there are **30 kilometers ****of ****tail** in each of them. But, if there were 4 towers open instead of two, and taking into account that there would be the same number of vehicles at the toll, how **many vehicles were there more or less for each pump tower** ? There would be **fewer vehicles** , because they would be distributed among more towers.

This is understood as if **increasing** the **number of towers** thus **decreases** the length of the **queue of vehicles** , and the **reverse** : if it had the **double towers have half queue** , and if there were half towers, would double tail . Showing that these quantities are **inversely proportional** .

## Other examples

- Juan has to buy black paint to give a previous coat to a room that wants to change color. If the paint container indicates that 8 m2 can be painted with 1 liter of paint, how
**many liters do**you**need in theory to be able to paint the walls of the room if it has 40 m2 of wall**? “ - A tap with a water outlet flow rate of about 18 liters per minute takes 14 hours to fill a domestic water tank. ¿
**How soon if its flow out of 7 liters per minute**? - A vehicle travels 270 km every 3 hours. How
**many kilometers will he have traveled in 2 hours**? - Yesterday 2 vans of a shipping company transported a merchandise from the port to its destination. Today 3 trucks, the same as yesterday, will have to make 6 trips to transport the same amount of merchandise from a warehouse to the port. How
**many trips did the trucks have to make yesterday**? - Upon arriving at the hotel, they gave a couple a map with the city’s attractions, and they have been told that 5 centimeters from the map represents 600 meters of reality. Today they wanted to go to a shopping center that is 8 centimeters from the hotel on the map. How
**far from the hotel is this shopping center**?

#### Answer

- Juan will therefore need 5 liters of black paint.
- With a tap of 7 liters per minute of flow we need at least 36 hours to fill the domestic water tank.
- In 2 hours it should travel 180 km
- Yesterday the 2 trucks made 9 trips each.
- The park is 960 meters from the shopping center.