Inverse Proportion

if two quantities are related in such a manner that if one quantity increases by a factor k and the other decreases by a factor of 1/k then the quantities are said to be inversely proportional.

In the case of hiring the van we say that

The product C x N is constant and the points lay on a curve of the form y = 1/x

__Example 1:__

Boyle’s Law states that at constant temperature, the volume **V** of a gas is inversely proportional to its pressure **P**. When the pressure is 600 N/m^{2} the volume is 4m^{3}. Find:

(a) The volume when the pressure is 400 N/m^{2}

(b) The pressure when the volume of the gas is 5 m^{3}

__Remember: Strategy for solving proportion problems__

1. Find the value of** k** (the constant of proportionality).

2. Use **k** together with **given values** to answer the question.

__Example 2:__

The cost **C** of hiring a transit van is inversely proportional to the number of people **N**, hiring it. If Robert hires the van himself, the cost will be £120. Find:

(a) The cost per person if a party of 4 people hire the van.

(b) The number of people hiring the van if the cost per person is £7.50.

__Example 3:__

The air pressure **P** that is delivered by a bicycle pump is inversely proportional to the square of its diameter **D**. If 8 units of pressure is delivered by a 20 mm diameter pump, find:

(a) The pressure delivered by an 18 mm pump.

(b) The diameter of a pump delivering 6 units of pressure.

*Your turn now!!*

The force of attraction F, between two magnets is inversely proportional to the square of their distance apart D. When the magnets are 2 cm apart the force of attraction is 24 units. Find:

(a) The force of attraction between two magnets that are 1/2 cm apart.

(b) The distance between two magnets when the force of attraction is 6 units.

That's all for this session in I/GCSE Mathematics.