The Rule of Three

This is used to find the value of a fourth quantity
when the relationship of two quantities is fixed and
the value of the third quantity is given.

For direct proportion:

• Align the data in correct columns
• Multiply 3rd data by 2nd
• Then divide by first.

The data must have the same units

Example

 Find x given A, B and a.

     

 

Example

If £4 is exchanged for $8.28, How many dollars will £15 be exchanged for ?

Example

A house has appreciated by 10%.
If it is now valued at £121,000, what was the original value ?

Example

A map has scale 3 : 50000
What is the real life distance to  a town if the distance on the map is 5.4 cm ?
Give your answer in kilometres.

Why does it work ?

This is effectively the same as finding the scale factor
and multiplying by the corresponding side:

 

For indirect proportion, go backwards:

• Align the data in correct columns
• Multiply first data by 2nd
• Then divide by third.

Example

If  it takes 4 days for 10 men to dig a trench,
how long will it take 8 men ?