The multi-choice question, for revision for 12 year olds, is here:
A company exchanges foreign currency. They offer $\$1.5$ for each pound. On top of this, they charge a fee of $£4.50$. Which formula shows the cost, $C$, in pounds of purchasing $\$D$? $${C = \frac{D}{1.5} + 4.5}$$ $${C = \frac{1.5}{D} + 4.5}$$ $${C = \frac{D}{1.5} + 450}$$
This seems considerably more complicated than the rest of the questions, in my opinion. But anyway, I would start by saying -
$${D = {1.5}C - 4.5}$$ ... which is equivalent to $${C = \frac{D + 4.5}{1.5}}$$ ... or more neatly $${C = \frac{2D}{3} + 3}$$ ... which is not one of the answers. The question is: is my mathematics flawed, or the BBC's?
If you use units (the exchange rate is $R = 1.5 \$ / 1£$ and the additional cost is $A = 4.5£$), you will see that the correct formula is $D = R (C - A) $.
In words, from the paid amount $C $ (the cost), the bank keeps the additional cost $A = 4.5£$ and exchanges the rest for the given exchange rate $R $.
Now rearranging will yield the first solution.
Different way of looking at it. You want to get $D $ dollars. This will normally cost you $D/R $ pounds (check the units!). But finally, the bank cares an additional fee of $A = 4.5 £$, so that we need to pay $4.5 £ + D /R $.