Question 1184984
w ounces of pure alcohol to add


{{{1*w+0.22*416=0.36(w+416)}}}--------this accounts for amount of pure alcohol.
Solve.


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The direction, to not use decimals seems unnecessary.   Do you really want the equation to start as   {{{w+(22/100)*416=(36/100)(w+416)}}} ?   You could do that, if you really want.


{{{w+(11/50)(416)=(9/25)(w+416)}}}{{{as_possible_first_step}}}

{{{w+(11/25)(208)=(9/25)(w+416)}}}

{{{25w+11*208=9(w+416)}}}

{{{25w+11*208=9w+9*416}}}

{{{16w=9*416-11*208=9*2*208-11*208}}}

{{{16w=7*208}}}

{{{w=7*13}}}

{{{highlight(w=91)}}}