Question

A bag of salt weighs \[2\dfrac{1}{4}\] kg. If \[40\dfrac{1}{2}\] kg of salt is to be put in such bags, how many bags will be required?

Answer 1

Hint: Here, with the help of unitary method, we will find that 1 kg of salt can be put in how many bags. Then, we will multiply both sides by \[40\dfrac{1}{2}\] to find the required number of bags which can carry this quantity of salt.

Complete step-by-step answer:
According to the question, a bag of salt weighs \[2\dfrac{1}{4}\] kg. Hence,
Weight of 1 bag \[ = 2\dfrac{1}{4} = \dfrac{9}{4}{\rm{kg}}\]
Now, by unitary method we can say that,
\[1{\rm{kg}}\] salt \[ = \dfrac{4}{9}\]bags
According to the questions, \[40\dfrac{1}{2}\] kg of salt is to be put in such bags.
Now, \[40\dfrac{1}{2} = \dfrac{{81}}{2}{\rm{kg}}\]
Since, \[1{\rm{kg}} = \dfrac{4}{9}\]bags
Therefore, \[40\dfrac{1}{2} = \dfrac{{81}}{2}{\rm{kg}}\] of salt will be put into :
\[\dfrac{{81}}{2} \times \dfrac{4}{9} = 2 \times 9 = 18\]bags
Hence, 18 bags are required to store \[40\dfrac{1}{2}\] kg of salt.

Note: Here, we have used a unitary method to solve this question. Unitary method is a technique in which we find the value of a single unit (say 1kg salt) and then, we find the required value by just multiplying it on both the sides of this single unit. Also, all the quantities were provided in mixed fraction hence, we were required to convert them to an improper fraction to solve this question. The method to convert a mixed fraction involved the multiplication of the whole number by the denominator of the given fraction and then, writing that number as a numerator by adding the existing numerator in the product. Hence, these two steps were essential to solve this question.