Can someone please help $me$ understand why the $dr$ solved $in$ such a way? i dont understand from where $he$ got the values nor how $he$ created and used the formulas

$6-34.$ Potable water $isin$ short supply $in$ many

countries. $To$ address this need, two mutually

exclusive water purification systems are being con$-$

sidered for implementation $in$ China. Doing nothing $is$

not $an$ option. Refer $to$ the data below and state your

key assumptions $in$ working this problem. $(6\mathrm{.}5)$

$a.$ Use the $PW$ method $to$ determine which system

should $be$ selected when MARR $-8\%$ per year.

$A=8\%$ per year.

$PW1(8\%)=-$$$100,000-$$$80,000(PF,8\%,5)+$$$20,000(PF,8\%,10)$

$+$$$28,000(\frac{P}{A}\mathrm{.}8\%\mathrm{.}10)$

$=$$$42,699$

$PW{W}_2(8\%)=-$$$150,000+$$$30,000(\frac{P}{A},8\%,10)=$$$51,303$

Therefore, select altemative $2to$ maximize profitability.

$B=15\%$ per year?

$P{W}_1(15\%)=$$$14,873P{W}_s(15\%)-$$$11590$