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]
