Question 200423
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
Working Eqn:
{{{B[1]+B[2]+B[3]=54v}}}


Conditions:


The voltage of 1st battery is twice the 2nd:
{{{B[1]=2B[2]}}} ---> {{{(1/2)B[1]=B[2]}}}, <font color=blue>A</font>


The 1st battery is 1/3 of the 3rd:
{{{B[1]=(1/3)B[3]}}} -----> {{{3B[1]=B[3]}}}, <font color=blue>B</font>


Subst. <font color=blue>A</font> & <font color=blue>B</font> in Working Eqn:
{{{B[1]+highlight((1/2)B[1])+highlight(3B[1])=54v}}}
{{{4.5B[1]=54v}}}
{{{cross(4.5)B[1]/cross(4.5)=cross(54)12v/cross(4.5)}}}
{{{red(B[1]=12v)}}}


Via conditions:
{{{12v=2B[2]}}} ---> {{{B[2]=12/2}}}
{{{red(B[2]=6v)}}}


{{{12v=(1/3)B[3]}}} ---> {{{B[3]=12*3}}}
{{{red(B[3]=36v)}}}


Check,
{{{12v+6v+36v=54v}}}
{{{54v=54v}}}


Thank you,
Jojo</font>