9 A craft artist is producing items and selling them in a local market.
The selling price, $\pounds P$, 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]
$\mathrm{\&}\ln$
9 (b) The production cost, $\pounds C$, 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 ：$24\times 10=k$

Step 3 ：$k=240$

Step 4 ：$P=\frac{240}{n}$

Step 5 ：$C{n}^2=k^{\prime }$

Step 6 ：$60\times {10}^2=k^{\prime }$

Step 7 ：$k^{\prime }=6000$

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