# Writing and using formulae

## In a nutshell

A formula can be created by analysing a question given in context. Questions can be based on calculations of physical quantities or geometrical measures.

*Note**: Remember to test the formula to see if it works, by substituting in values.*

## Making a formula

To make a formula, read the information given, give the unknown quantity a letter name and use your knowledge of algebra to give the formula.

##### Example 1

*Write a formula for the cost, c, of n boxes of chocolate at £2 each.*

$c=2n$

*If there are 3 boxes, *$n=3$*, so*

$c=2n = 2 \times 3 = 6$

*So the total cost is* $\underline{£6}$.

##### Example 2

*Write a formula for the age of Fred, f, who is four years older than George, g.*

*You can write the formula is 2 different ways, Fred's age is four more than George's age, or George's age is four less than Fred's age. *

$\underline {f=g+4}$ or $\underline{g=f-4}$

##### Example 3

*A restaurant charges* $£C$ *for delivering pizzas, through a delivery app. They charge a standard fee of* $£1.50$ *and an additional charge of* $80p$ *for each mile, m, travelled. Write a formula for* $C$.

$\underline{C=0.8m+1.5}$

*Note:** Remember to convert to the same units if necessary, in this case *$80p$* has been converted to *$£0.8$*.*

##### Example 4

*A rectangle has length* $4cm$ *more than width. Write a formula for the area.*

$\begin {aligned}A&= width \times length \\A&= x(x+4) \\ \end {aligned}$

$\underline {A= x^2 + 4x}$