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The Rule of Three

The Rule of Three 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 known.

For direct proportion:

The data must have the same units.

Example

Find \(x\) given \(A\), \(B\) and \(a\).

Example 1

More Direct Proportion Examples

Example

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

Example 2
Example

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

Example 3
Example

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

Example 4

Why does it work?

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

Scale factor explanation Scale factor formula

Indirect Proportion

For indirect proportion, go backwards:

  • Align the data in correct columns
  • Multiply the 1st data by the 2nd
  • Then divide by the 3rd
Indirect proportion layout
Example

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

Example 5