Question

Half a swarm of bees went to collect honey from a mustard field. Three fourth of the rest went to a rose garden. The rest ten were still undecided. How many bees were there in all

Answer 1

Therefore, their were 80 bees in all.

Answer 2

There are total of 80 bees in the swarm.

Step-by-step explanation:

Let the total number of bees in the swarm be 'x'.

Now according to question,

Half a swarm of bees went to collect honey from a mustard field.

number of bees went to collect honey from a mustard field = $\frac{x}{2}$

Also Given:

Three fourth of the rest went to a rose garden.

number of bees went to rose garden = $\frac{3}{4}(x-\frac{x}2})$

Number of bees undecided = 10

Now we know that;

total number of bees is equal to sum of number of bees went to collect honey from a mustard field and number of bees went to rose garden and Number of bees undecided.

framing in equation form we get;

$\frac{x}{2}+\frac{3}{4}(x-\frac{x}{2})+10 = x\\\\\frac{x}{2}+\frac{3}{4}x-\frac{3}{4}\times \frac{x}{2} =x-10\\\\\frac{x}{2}+\frac{3}{4}x-\frac{3x}{8} =x-10$

Now making the denominator common using LCM we get;

$\frac{x\times4}{2\times4}+\frac{3\times2}{4\times2}x-\frac{3x\times1}{8\times1} =x-10\\\\\frac{4x}{8}+\frac{6x}{8}-\frac{3x}{8} =x-10\\\\\frac{4x+6x-3x}{8} = x-10\\\\7x=8(x-10)\\\\7x= 8x -80\\\\8x-7x=80\\\\x=80$

Hence there are total of 80 bees in the swarm.