Question 1102016
---------------------------------------------------------------------
A calls for one-third less than twice the number of cups of sugar that recipe B calls for.
---------------------------------------------------------------------


{{{A=2B-(1/3)2B}}}



---------------------------------------------------------------------
he needs four and one-sixths cups of sugar in all, 
---------------------------------------------------------------------


{{{A+B=4&1/6}}}



First substituting for A, solve for B, and then evaluating A, seems the clearest way.


But since question asks for A,...
{{{system(A=2B-(1/3)B,A+B=4&1/6)}}}


{{{3A=6B-B}}}
{{{3A=5B}}}
{{{B=(3/5)A}}}
-
{{{A+(3/5)A=4&1/6}}}, LCD is 30...

{{{A+(3/5)A=25/6}}}

multiply left and right by 30...
{{{30A+18A=25*5}}}

{{{48A=125}}}

{{{A=125/48}}}

{{{highlight(A=2&2/3)}}}