## 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

IfÂ it takes 4 days for 10 men to dig a trench,

how long will it take 8 men ?

© Alexander Forrest