Question

One-fifth of a hive of bees flew to the Kadamba flower; one-third flew to the Silandhara; three times the difference of these two numbers flew to an arbor, and one bee continued flying about, attracted on each side by the fragrant Keteki and the Malati. Find the number of bees.

Answer 1

Answer: $15\ bees$

Step-by-step explanation:

Let be "x" the number of bees of the hive,

You know that One-fifth of bees flew to the  Kadamba flower. This can be represented with this expression:

$\frac{1}{5}x$

One-third of the bees flew to the Silandhara. This is:

$\frac{1}{3}x$

 Three times (This indicates multiplication) the difference  of these two number of bees (This indicates subtraction) flew to an arbor.  Then, this can be represented as:

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

Having this information and knowing that one bee continued flying about, you can write the following equation in order to find the value of "x":

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

Solving for "x", you get:

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

Answer 2

The total number of bees in total that flew to the different locations anc continued flying is; 15 bees

How to solve fractions?

Let x be the number of bees in the hive,

We are told that One-fifth of the bees flew to the  Kadamba flower. Thus;

Number of bees that flew to kadamba = ¹/₅x

one-third flew to the Silandhar and this is; ¹/₃x

Three times the difference of these two numbers flew to an arbor, and one bee continued flying about.

Thus;

¹/₅x + ¹/₃x + 3(¹/₃x - ¹/₅x) + 1 = x

¹/₅x + ¹/₃x + x - ³/₅x + 1 = x

Multiply through by 15 to get;

3x + 5x + 15x - 9x + 15 = 15x

3x + 5x + 15x - 9x - 15x = -15

x = 15

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