How to solve a sample GCSE exam question

I recently wrote an article for the Bristol Pigeon. In it I asked readers to solve the following question, which was taken from the AQA June 2017 non-calculator paper.

Having thoroughly read the question, and noted the number of marks allocated, the first thing to do is to try and condense the words into the beginnings of some maths. It doesn’t matter at this stage if you still have words in there are well, the important thing is to get something down on paper.

We need to calculate the number of females in the office and the number of males, as if we know these two numbers, we know the answer. (The AQA world does not contain transgender people). So lets begin here:

The first sentence of the question, can be simplified to:

The next line, “1/4 of the females wear glasses”, can be summarised:

and likewise, “3/8 of the males wear glasses” as:

The last bit of information the question tells us, “84 people in the office wear glasses”. As the number of people wearing glasses is the number of females wearing glasses plus the number of males wearing glasses, we can use the 2 previous bits of information to form another equation:

Finally, lets note down an expression for the total number of people in the office:

Now we are ready to solve it! It is good practice to label any equations you generate with numbers . This makes them easy to refer to later on.

Equations 1 and 2 contain enough information to solve for f and m. Substituting 1 into 2, gives an expression containing only m:

Note, students are expected to work out 84 x 8/7, which is much easier if you can know that 84 is a multiple of 7 and cancel it down to 12.

So there are 96 men in the office. Use equation 1 to work out how many females:

All that remains is to use equation 3 to get the answer:

So it turns out this is large office containing 288 people. Congratulations if you got it correct!