Three brine solutions, B$1,$ B$2,$ B$3,$ are mixed. B$1$ is one$-$half of the total mixture. Brine B$1$ is $2\mathrm{.}5\%$ salt, B$2$ is $4\mathrm{.}5\%$ salt, and B$3$ is $5\mathrm{.}5\%$ salt. To this mixture is added $22lbm$ of dry salt while $179lbm$ of water is evaporated leaving $1,500lbm$ of $5\mathrm{.}1\%$ brine. Determine the initial amounts of B$1,$ B$2,$ and B$3.($Round the final answer to three decimal places.$)$

$($a$)$ The initial amount of $B1=$ lbm$.$

$($b$)$ The initial amount of $B2=$ Ibm.

$($c$)$ The initial amount of $B3=$ Ibm.