Mathematical inequalities in real life

Often in real life we find ourselves in situations that can be represented mathematically by inequalities. For example, if we want to take a taxi, we may find that the charge is £1.50 standard charge plus 50p per mile. If we only have £20, then we can describe the situation with the following inequality:

£1.5 + £0.5\({M}\) \({\leq}\) £20

\({M}\) = number of miles travelled.

When constructing inequalities it is important that we understand what it is we are trying to achieve and, most importantly, which inequality sign we should use.

Example

A school is holding a cake sale to raise money. They are selling cakes for £1 and soft drinks for 50p. Write an inequality to show how many cakes and drinks they must sell to make at least £100.

They make 50p for each soft drink – £0.5 × \({d}\)

They make £1 for each cake - £1 × \({c}\)

So the inequality is:

(£0.5 × \({d}\)) + (£1 x \({c}\)) \({\geq}\) £100

Question

Kayleigh has £200. She wants to buy some games for her PC which cost £30 each, but she also wants to have at least £75 left. Write an inequality for this situation using \({n}\) to represent the number of games she can buy.

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Inequalities - Intermediate & Higher tier – WJECMathematical inequalities in real life