A sports store purchased tennis racquets for $$45\mathrm{.}84$ less $41\%$ for purchasing more than $100$ items, and a further $31\%$

was reduced for purchasing the racquets in October. The racquets were sold to customers for $$56\mathrm{.}99.$

$($a$)$ What is the cost of each racquet?

$($b$)$ What is the markup as a percent of cost$?$

$($c$)$ What is the markup as a percent of selling price?

$($a$)$ The cost of each racquet is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places

as needed.$)$