Here’s a practice question in long maths with detailed step-by-step solution.  Long maths is in the CEM 11+ exam, but mathematics questions like the one below appear in selective school exams and scholarship exams too.  Let’s go through it.

A flight to Japan costs £300 for an adult one way and for a child, it’s 50% of an adult fee. A return flight to Japan is 150% the cost of a one-way ticket. All flights have a compulsory additional 10% fee surcharge for taxes that is added to the end total. What is the cost for 2 adults and 1 child to fly return to Japan?

1) What is the actual question asking you to do?

The question is what is the cost for 2 adults + 1 child to fly return to Japan.  The stuff before that is the information you will need to answer it.  Just be clear on this because it helps you to focus what you are working towards.

2) Break it down into components - adult fares, child fare and taxes.

What’s the cost for an adult return?  £300 is one way and a return is 150% of this.  We know that 50% of £300 is £150.  So £300 + £150 = £450 and that’s the cost of an adult return flight.  We need two of those, so it’s £450 x 2 = £900.

What’s the cost of a child return?  We know that a child ticket is 50% of an adult ticket so let’s apply the return adult ticket of £450.  £450 x 50% = £225.

So the total tickets (2 adults and 1 child) is £1125.  We also need to add 10% tax on top of that.  The easiest way to calculate a percentage, especially when it is in tenths is moving the decimal point.  We know that it would be 2 decimal points to the left for 10% of 100 so with 1000, it’s one decimal point.

£1125 x 10% = £112.5.  So altogether, it’s £1125 + £112.5 = ****£****1237.50****

So in two steps and four substeps, we’ve come to the answer!  It’s £1237.50

See how by breaking things down into smaller components, you’ll be able to see clearly how you get to the answer so if there are any corrections that need to be made, you’ll be able to identify and fix it.

Workings are extremely important.