Question

Farida bought some bags of cement, each weighing \[49.8{\text{ kg}}\]. If the total weight of all the bags is \[1792.8{\text{ kg}}\]. How many bags did she buy?

Answer 1

Hint: Here we will calculate the answer by dividing the total weight of the items by the weight of each item, for example, if the total weight of any number of items is
\[x{\text{ kg}}\]and the weight of each item is
\[{\text{y kg}}\]then the number of items will be equals to as below:
\[{\text{Number of items}} = \dfrac{x}{y}\].

Complete step-by-step solution:
Step 1: It is given that the total weight of the cement bags is \[1792.8{\text{ kg}}\] and each bag weighs
\[49.8{\text{ kg}}\].
So, for calculating the number of bags, we will divide the total weight of all bags by the weight of each bag as shown below:
\[ \Rightarrow {\text{Number of items}} = \dfrac{{1792.8}}{{49.8}}\]
By writing the term
\[1792.8 = \dfrac{{17928}}{{10}}\] and
\[49.8 = \dfrac{{498}}{{10}}\] in the above expression we get:
\[ \Rightarrow {\text{Number of items}} = \dfrac{{17928 \times 10}}{{498 \times 10}}\]
By dividing the numerator and denominator of the RHS side by \[6\] we get:
\[ \Rightarrow {\text{Number of items}} = \dfrac{{2988 \times 10}}{{83 \times 10}}\]
By dividing the numerator and denominator of the RHS side by \[83\] we get:
\[ \Rightarrow {\text{Number of items}} = \dfrac{{36 \times 10}}{{10}}\]
Eliminating \[10\] from the RHS side of the above expression we get:
\[ \Rightarrow {\text{Number of items}} = 36\]

Total number of items are \[36\].

Note: Students need to take care while solving the expression. Also, the number of items will be equal to the total weight divided by each item's weight, not vice versa.