9 A craft artist is producing items and selling them in a local market.
The selling price, $£ P$, of an item is inversely proportional to the number of items produced, $n$
9 (a) When $n=10, P=24$
Show that $P=\frac{240}{n}$
[1 mark]
$\& \ln$
9 (b) The production cost, $£ C$, of an item is inversely proportional to the square of the number of items produced, $n$
When $n=10, C=60$
Find the set of values of $n$ for which $P> C$
[4 marks]

Step 1 ：\(Pn=k\)

Step 2 ：\(24\times10=k\)

Step 3 ：\(k=240\)

Step 4 ：\(P=\frac{240}{n}\)

Step 5 ：\(Cn^2=k'\)

Step 6 ：\(60\times10^2=k'\)

Step 7 ：\(k'=6000\)

Step 8 ：\(C=\frac{6000}{n^2}\)

Step 9 ：\(P>C\)

Step 10 ：\(\frac{240}{n}>\frac{6000}{n^2}\)

Step 11 ：\(n^2>25n\)

Step 12 ：\(n^2-25n>0\)

Step 13 ：\(n(n-25)>0\)

Step 14 ：\boxed{0