# Substitution

When letters in a formula are replaced by numbers, it is called substitution.

## Example - time

For the purpose of measuring time, the Earth's surface is divided into equal wedges of , each called a time zone, beginning at Greenwich, London (GMT). As you pass over each zone to the east you add hour to GMT, and as you pass over each zone to the west you subtract hour from GMT.

On this basis, call the time in London ' '.

The formula for working out the time in Bangkok, Thailand, is .

And the formula for working out the time in Santiago, Chile, is .

These formulae allow us to substitute for any time in London to find out the time in Bangkok or Santiago.

Question

Q1. Using the formula above, find the time in Bangkok when it is hours in London.

Q2. What time is it in Santiago, Chile, when the time in London is hours?

A1. Time in Bangkok .

Substitute the for the . So at hours in London, the time in Bangkok is hours.

A2. The formula for working out the time in Santiago is: When : So at hours in London, the time in Santiago is hours.

## Example - temperature

Here is the formula to convert the temperature in degrees Fahrenheit to the temperature in degrees Celsius : where represents the temperature in and represents the temperature in .

This formula allows you to substitute any temperature for to find its equivalent temperature in .

### Example

To find the temperature in when it is , substitute for the in the formula.

When ,  Remember to work out any calculation in brackets first: A number next to anything in brackets means the contents of the brackets should be multiplied, so means :   So Question

What is the temperature in when it is ? Therefore: 