Final answer:
The cross exchange rate between the British pound (£) and the US dollar ($) is £1 = $1.25, calculated by dividing the given S(£/AUD) by S($/AUD).
Step-by-step explanation:
The cross exchange rate between the pound (£) and the dollar ($) can be calculated using the given direct quotes of $/AUD and £/AUD. Since S($/AUD) = 0.8 and S(£/AUD) = 0.5, we use these rates to find the value of one currency in terms of the other.
The formula for the cross exchange rate, S(£/$), is given by dividing the AUD/£ rate by the AUD/$ rate. This is because we want to find out how many dollars we can get for one pound, and we know how many Australian dollars we can get for each of the two currencies. So, the cross exchange rate S(£/$) is 0.5 AUD/£ divided by 0.8 AUD/$ which equals £1 = $1.25.