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 {24} equal wedges of {15}^\circ, each called a time zone, beginning at Greenwich, London (GMT). As you pass over each zone to the east you add {1} hour to GMT, and as you pass over each zone to the west you subtract {1} hour from GMT.

On this basis, call the time in London ' {g}'.

The formula for working out the time in Bangkok, Thailand, is g + 7.

And the formula for working out the time in Santiago, Chile, is g - 4.

These formulae allow us to substitute {g} 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 \text{14:00} hours in London.

Q2. What time is it in Santiago, Chile, when the time in London is \text{20:00} hours?

A1. Time in Bangkok = g + 7.

Substitute the {14} for the {g}.

g + 7 = 14 + 7 = 21

So at \text{14:00} hours in London, the time in Bangkok is \text{21:00} hours.

A2. The formula for working out the time in Santiago is:

g - 4

When g = 20:

g - 4 = 20 - 4 = 16

So at \text{20:00} hours in London, the time in Santiago is \text{16:00} hours.

Example - temperature

Here is the formula to convert the temperature in degrees Fahrenheit (^\circ{F}) to the temperature in degrees Celsius (^\circ{C}):

c = \frac {5(f - 32)} {9}

where {f} represents the temperature in ^\circ{F} and {c} represents the temperature in ^\circ{C}.

This formula allows you to substitute any ^\circ{F} temperature for {f} to find its equivalent temperature in ^\circ{C}.

Example

To find the temperature in ^\circ{C} when it is {68}^\circ{F}, substitute {68} for the {f} in the formula.

When f = 68,

{c}=\frac{5(f-32)}{9}

{c}=\frac{5(68-32)}{9}

Remember to work out any calculation in brackets first: (68 - 32) = 36

A number next to anything in brackets means the contents of the brackets should be multiplied, so 5(36) means 5 \times 36:

{c}=\frac{5(36)}{9}

{c}=\frac{5\times36}{9}

{c}=\frac{180}{9}=20

So {68}^\circ{F}={20}^\circ{C}

Question

What is the temperature in ^\circ{C} when it is {77}^\circ{F}?

{c}=\frac {5(77 -32)}{9} = \frac {5 \times 45}{9} = 25

Therefore:

{77}^\circ{F}={25}^\circ{C}