A manufacturer of briquettes has a contract to make briquettes for barbecuing that are guaranteed to not contain over $10\%$ moisture or $10\%$ ash. The basic material used has this analysis: moisture $12\mathrm{.}5\%,$ volatile material $16\mathrm{.}8\%,$ carbon $57\mathrm{.}3\%,$ and ash $13\mathrm{.}4\%.$ To meet the specifications $($at their limits$),$ the manufacturer plans to mix with the base material a certain amount of petroleum coke that has this analysis: volatile material $8\mathrm{.}4\%,$ carbon $88\mathrm{.}4\%,$ and moisture $3\mathrm{.}2\%.$ How much petroleum coke must be added per $50$ kg of the base material?