Question 957827
Multiply both sides by {{{5*12=60}}}
{{{60(3y)-(5*12)(8/12) = (5*12)(y/5)}}}
{{{180y-40=12y}}}
Add {{{-12y}}} to both sides,
{{{180y-12y-40=12y-12y}}}
{{{168y-40=0}}}
Add {{{40}}} to both sides,
{{{168y-40+40=40}}}
{{{168y+0=40}}}
{{{168y=40}}}
Divide both sides by {{{168}}}
{{{(168y)/168=40/168}}}
{{{(168/168)y=40/168}}}
{{{(1)y=40/168}}}
{{{y=40/168}}}
Factor out any common factors in numerator and denominator,
{{{y=(8*5)/(8*21)}}}
{{{y=(8/8)(5/21)}}}
{{{y=5/21}}}
That's the solution to the problem as written, however it's not a proportion.
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Just in case if the problem was,
{{{(3y-8)/12=y/5}}}
Then, multiply both sides by {{{60}}}.
{{{5(3y-8)=12y}}}
Distribute the {{{5}}}} on the left hand side.
{{{15y-40=12y}}}
Subtract {{{12y}}} from both sides,
{{{15y-12y-40=12y-12y}}}
{{{3y-40=0}}}
Add {{{40}}} to both sides,
{{{3y-40+40=40}}}
{{{3y+0=40}}}
{{{3y=40}}}
Divide both sides by {{{3}}}.
{{{(3y)/3=40/3}}}
{{{(3/3)y=40/3}}}
{{{(1)y=40/3}}}
{{{y=40/3}}}