QTS Numeracy Model Solutions – Test 2, Q18

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the Department for Education.

In this post, we look at question 18 from practice test 2. The full practice paper can be downloaded here​.

The Question

A teacher is planning a group outing to see a play in a nearby city.

She has been given details of costs and travel.

There are 25 in the group, including pupils and teachers.

A group booking for 25 theatre tickets costs £185.

Return train tickets cost £5.65 each.

How much will each person have to pay for the outing to cover the cost of travel and theatre ticket?

Worked Solution

Questions like this come up quite often on the QTS Numeracy Test, and they can initially seem daunting because your are presented with so many details in the question that it may not be apparent where to start.

With a question like this, it is worth taking a moment or two to read (and then re-read) the question. Before you get started with the calculation, you want to get clear on two things: What is the situation that the question is describing, and what exactly are you being asked to work out.

The situation is made clear in the first couple of sentences – a teacher is planning a theatre trip for a group, that will involve costs for both the theatre and the travel.

The last sentence gives you the question – you need to know how much each person will need to pay, so this is a question that deals with the topic of money.

You are looking for how much each person will pay, and this actually makes the calculation more straight forward than it otherwise would have been. All you need to do is find out the theatre cost per person and the travel cost per person and add these values together.

In the penultimate line of the question, you are told that the cost of train tickets is £5.65 per person, so you now only need to work out how much each person will pay for the theatre.

The question says that the total cost for the group is £185, and this cost is shared between 25 people, so to find how much each person pays you can divide £185 by 25.

£185 ÷ 25 = £7.40

This means that the total cost for an individual would be £5.65 + £7.40 = £13.05

Note: Another way of approaching this question would have been to work out the total cost of theatre tickets and travel for the entire group and then divide this answer by 25. However, this would have been a longer and more complicated method than the approach used in this model solution.

Final Answer: £13.05

Note – I have made a point of being thorough in this method to ensure you understand each point as we go. When you sit your QTS Skills Tests, your process will probably be much quicker as these techniques start to become second nature to you.

Further Help

If you require any further help with questions like this, we have created a selection of resources to provide all the help you need.

Revision Book – The Guide to the QTS Skills Tests book devotes a whole chapter to each QTS numeracy topic, with detailed methods, worked examples and plenty of practice questions for you to have a go at. The book also includes three practice tests and fully worked solutions to every question.

Practice Tests – Want more practice tests to see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test (including some totally free papers as our gift to you).

Revision Cheat Sheets – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!