so solve for z
we cannot know what x and y are so we must make it equal to z so
(x/100)+(y/66)=(3x+5y)/z
multiply both sides by z/(3x+5y)
(z/(3x+5y))((x/100)+(y/66))=1
divide both sides by ((x/100)+(y/66))
z/(3x+5y)=1/((x/100)+(y/66))
multiply both sides by (3x+5y) to clear fraction (because x/4 times 4=x/1 times 4/4=x)
so
z=(3x+5y)/((x/100)+(y/66))