Anna purchased $31$ strings for her autoharp. Wrapped strings cost $$4\mathrm{.}99$ each and unwrapped strings cost $$3\mathrm{.}49$ each. If she paid a total of $$133\mathrm{.}69$ for the strings, how many of each type did she buy?

Anna purchased wrapped strings and unwrapped strings.

$($Simplify your answers.$)$