2008 TJC P1 Q5

A certain supermarket sells only three brands of health drinks namely Mud, Soil and Rock which are priced at \(\$2.00\), \(\$1.80\) and \(\$1.50\) per bottle respectively.

Discounts offered for each brand as follows:

\(20\%\) discount when more than \(80\) bottles of Mud are bought;

\(15\%\) discount when more than \(50\) bottles of Soil are bought;

\(10\%\) discount when more than \(30\) bottles of Rock are bought.

Andy orders \(200\) bottles of health drinks from the supermarket for a company function. As the preference for each brand differs among the colleagues in the company, he has to order at least \(60\) bottles of each of the \(3\) brands.

Andy spent \(\$323.05\) after an overall discount of \(\$27.45\).

Find the number of bottles of each brand Andy bought from the supermarket, explaining your answer clearly.