Question $3($Bituminous mixture weight$-$volume calculations$)$

From laboratory tests, the following results have been obtained.

$>$ Weight of dry compacted specimen in air $=1174\mathrm{.}4g$

$>$ Weight of SSD specimen in air $=1177\mathrm{.}3g$

$>$ Weight of compacted specimen in water $=677\mathrm{.}2g$

$>$ Maximum theoretical specific gravity of mix$=2\mathrm{.}438$

The bulk specific gravities of coarse aggregate, fine aggregate and mineral filler are respectively $2\mathrm{.}606,2\mathrm{.}711$ and $2\mathrm{.}697.$ The specific gravity of asphalt is $1\mathrm{.}010.$ The mix composition in percent by weight of total mix is as follows: $6\mathrm{.}96\%$ asphalt, $51\mathrm{.}45\%$ coarse aggregate, $34\mathrm{.}24\%$ fine aggregate, and $7\mathrm{.}35\%$ mineral filler. Determine:

$($a$)$ Bulk specific gravity of total aggregate