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.

	$x+4$
$x$

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

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