Forming equations

Foundation and Higher

The idea

Choose a letter for the unknown, write each quantity in terms of it, then use the fact you are given to write an equation.

Let $x$ be the unknown and say what it stands for.
Write the other quantities from it, for example angles $x$ , $2x$ and $x + 30$ .
Use the given fact (angles in a triangle add to $180^\circ$ ), solve, then answer the question.

Watch out Finish by answering what was asked: often it is not $x$ itself but one of the quantities.

See it worked

Worked exampleNon-calculator3 marks

Zara thinks of a number. She doubles it and then adds 7. Her answer is 31.

Form an equation and solve it to find Zara's number. You must show your working.

Let the number be $n$ . $2n + 7 = 31$
Solve. $2n = 24 \Rightarrow n = 12$

Answer $12$

Your turn

Question 1Calculator allowed3 marks

A theatre sells adult tickets for £12 and child tickets for £7. A group buys 9 tickets for £88. How many adult tickets does the group buy?

Question 2Calculator allowed3 marks

A tank contains 12 litres of a mixture that is 20% concentrate by volume. A second mixture is 45% concentrate. How many litres of the second mixture must be added to make a mixture that is 30% concentrate? Assume volumes add. You must show your working.

Question 3Calculator allowed4 marks

A small auditorium has 330 seats arranged in rows. Each row has 3 more seats than the row immediately in front. The back row has three times as many seats as the front row. Work out the number of rows. You may use: sum of an arithmetic sequence = $\frac{1}{2}$ $\times$ number of terms $\times$ (first term + last term).

In past papers

201 official questions in 148 papers since 2017. The latest:

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