## 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 ? 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 ?  © Alexander Forrest