(a)[3]
Each chocolate bar is $p$ cents and each packet of sweets costs $75$ cents. Tanish spends $9.10$ on $5$ chocolate bars and $8$ packets of sweets. Set up an equation and solve it to determine $p$. Show your working.
(b)[2]
Factorise $6ac - 27c$ into brackets.
(c)[2]
Write $\frac{3m^2n}{10} \times \frac{5n}{9m}$ as one fraction, then simplify it fully.
(d)[2]
Rearrange the formula $y = \frac{3x^2}{5}$ so that $x$ is the subject.
(e)[4]
A collection of $k$ numbers has a mean of $56.8$. The number $52$ is added to the collection. The updated mean becomes $56.5$. Determine the value of $k$.