From November to December of $2015,$ the price per share of BP Oil dropped from $$95\mathrm{.}75$ to $$83\mathrm{.}25.$ Exxon shares also dropped from $$98\mathrm{.}75$ to $$76\mathrm{.}75.$

In November, your rich cousin invested $$85,658\mathrm{.}75$ into a combination of BP and Exxon shares. By December they sold their shares for $$72,845\mathrm{.}75$ losing $$12,813$ from their investment.

How many of each stock did they purchase?

They purchased $BP$ shares and $$ Exxon shares.