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 $$\underline{£6}$$.

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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.

	​$$x+4$$​​
​$$x$$​​

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

​$$\underline {A= x^2 + 4x}$$​​