One-fifth of a swarm of bees is resting on a kadaba bush and a third on a silindha bush; three timesthe difference between these two numbers is on a kutaja, and a single bee has flown off in the breeze drawn by the odor of a jasmine and a pandam. Tell me, beautiful maiden, how many bees are there?

Answer:There are 15 bees.Step-by-step explanation:Let's call x the total number of bees. There is one fifth of that in one bush, which can be written as:[tex]\frac{1}{5}x[/tex]there is one third on another, which is:[tex]\frac{1}{3} x[/tex]the other one has three times the difference between the previous two:[tex]3(\frac{1}{3}x-\frac{1}{5}x)[/tex]So, if we add those three quantities plus one single bee that flew away, it all should add up to the total number of bees, which is x. So:[tex]3(\frac{1}{3}x-\frac{1}{5}x)+\frac{1}{3}x+\frac{1}{5}x+1=x[/tex]We will solve for x:[tex]\frac{3}{3}x-\frac{3}{5}x+\frac{1}{3}x+\frac{1}{5}x+1=x[/tex][tex]\frac{15}{15}x-\frac{9}{15}x+\frac{5}{15}x+\frac{3}{15}x+1=x[/tex][tex]\frac{14}{15}x+1=x[/tex]We will move the positive x on the right of the equal as a negative one to the left:[tex]\frac{14}{15}x-x+1=0[/tex][tex]\frac{14}{15}x-\frac{15}{15}x+1=0[/tex][tex]-\frac{1}{15}x+1=0[/tex][tex]1=\frac{1}{15}x[/tex][tex]15=x[/tex]We can prove this answer by replacing in the original equation:[tex]3(\frac{1}{3}15-\frac{1}{5}15)+\frac{1}{3}15+\frac{1}{5}15+1[/tex][tex]3(5-3)+5+3+1[/tex][tex]3(2)+9[/tex][tex]6+9=15[/tex]