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**Hint:**Now let us say that n buckets are needed to fill 586.5 litres of water. Now we know that the water in n buckets will be n × capacity of water in 11 buckets. Here we know that 1 bucket has a capacity of 8.5 litres. Hence substituting this in the equation we will find the value of n and hence find the number of buckets needed.

**Complete step by step solution:**

Now we are given that the capacity of the bucket is 8.5 litres. Now we know that one bucket will hold 8.5 litres of water. 2 buckets will hold 2 × 8.5 litres of water and hence n buckets will hold $n\times 8.5$ litres of water.

Now we are given that there is 586.5 litres of water.

Now let us say n buckets of water are filled with 586.5 litres of water.

Now the water in n buckets is given by n × 18.5 litres.

But we know that the water in n buckets is 586.5 litres.

Hence we have the equation n × 18.5 = 586.5.

Now dividing the whole equation by 18.5 we get,

$\Rightarrow n=\dfrac{586.5}{18.5}$

Now multiplying the numerator and denominator to remove the decimal we get,

$n=\dfrac{5865}{185}=31.70$

Now since n is the number of buckets n must be a natural number.

**Hence we will need at least 32 buckets to fill 586.5 litres of water.**

**Note:**Now note that we can always use a unitary method to solve this type of equation. Here we have, 1 bucket holds 18.5litres so how many buckets hold 586.5. Let the number of buckets be x. then we take the ratio as $\dfrac{18.5}{1}=\dfrac{586.5}{x}$. Also note that since n must be an integer we will take n to be the next integer close to the obtained number.

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