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 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.