General Systems, a computer manufacturer, announces that it will be acquiring FastWorks Software. You know the following $$

$$ General Systems had a levered beta of $1\mathrm{.}09$ prior to the merger. The firm has a market value of equity of $$12$ billion and $$16$ billion in debt outstanding.

$$ FastWorks Software had a levered beta of $1\mathrm{.}30$ prior to the merger. The firm has a market value of equity of $$6\mathrm{.}00$ billion and $$6\mathrm{.}00$ billion in debt outstanding.

a$)$ Estimate the unlevered beta of the combined firm.

b$)$ If you were told that the combined firm$$s levered beta will be $1\mathrm{.}270$ after the acquisition, how much debt did General Systems use to acquire FastWorks? $[$You can assume that General Systems will assume Fastworks$$ existing debt$].$ Both firms have a $40\mathrm{.}00\%$Tax rate