Question

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 1

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:

$\frac{1}{5}x$

there is one third on another, which is:

$\frac{1}{3} x$

the other one has three times the difference between the previous two:

$3(\frac{1}{3}x-\frac{1}{5}x)$

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:

$3(\frac{1}{3}x-\frac{1}{5}x)+\frac{1}{3}x+\frac{1}{5}x+1=x$

We will solve for x:

$\frac{3}{3}x-\frac{3}{5}x+\frac{1}{3}x+\frac{1}{5}x+1=x$

$\frac{15}{15}x-\frac{9}{15}x+\frac{5}{15}x+\frac{3}{15}x+1=x$

$\frac{14}{15}x+1=x$

We will move the positive x on the right of the equal as a negative one to the left:

$\frac{14}{15}x-x+1=0$

$\frac{14}{15}x-\frac{15}{15}x+1=0$

$-\frac{1}{15}x+1=0$

$1=\frac{1}{15}x$

$15=x$

We can prove this answer by replacing in the original equation:

$3(\frac{1}{3}15-\frac{1}{5}15)+\frac{1}{3}15+\frac{1}{5}15+1$

$3(5-3)+5+3+1$

$3(2)+9$

$6+9=15$