2. The rule of three direct

After we know what the value of a unit is, we can also know what the values of other units are. In these cases, we must apply the rule of three.
For example: 3 packs of cigarettes cost 6 Euros. How much money will 10 packs cost?
We have three numbers and we need another one that is the unknown quantity.

If 3 packets (A) cost 6 Euros (B)
10 packs (C) will cost x (D)

A package will cost 2 Euros (6:3) and 10 packs will cost 20 Euros (2 x 10). We also multiply (6 x 10) and we divide it by 3. The result is 20 Euros.
When we solve the problem by the rule of three, first we must multiply the numbers B and C and the we divide it by A (6 x 10): 3 = 20 Euros.
We must check that the quantities A and C are of the same species. In this case they are packets.

For example: We have driven 560 kilometers in 8 hours. How many kilometers will we go over in 12 hours?

In 8 hours (A) ------ > 560 km (B)
In 12 hours (C) ------ > x (D)

x = (560 x 12)
: 8 = 6720 : 8 = 840 kilómetros.

In general, the rule of three with directly proportional magnitudes is solved by multiplying B and C and by dividing it by A.

Solve these problems: :

3. The rule of three inverse

In inversely proportional magnitudes, when one amount increases, the other one decreases.
Example: The speed of a car and the time it takes to travel a distance. The more speed, the less time it takes.

For example: 12 builders build a house in 60 days. How long will it take the two builders build it?

12 builders (A) take 60 days (B)
2 builders (B) take x (D)

One builder will only take (12 x 60) = 720 days. Two builders will take 720:2 = 360 days.
With the rule of three, we multiply A and B and then we divide it by C.
D = (A x B): C

In general, the rule of three with inversely proportional magnitudes is solved by multiplying A and B and by dividing it by C.

Solve these problems:

4. Review of the rule of three

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®Arturo Ramo García.-Record of intellectual property of Teruel (Spain)
No 141, of 29-IX-1999
Plaza Playa de Aro, 3, 1º DO 44002-TERUEL