Question

If the weight of 12 sheets of thick paper is 40grams, how many sheets of the same paper would weigh \[16\dfrac{2}{3}\] kilograms?

Answer 1

Hint: We will solve this problem by unitary method. We are given with the weight of 12 sheets of paper but in grams and we are asked to find how many such sheets would weigh \[16\dfrac{2}{3}\] kilograms. Now very first we will make the units of weight the same and then using the unitary method we will find the number of sheets.

Complete step-by-step answer:
Given that the weight of 12 sheets of thick paper is 40grams.
\[
  12sheets \to 40grams \\
  1sheet \to ? \\
   \Rightarrow ?(1sheet) = \dfrac{{40}}{{12}}grams \\
\]
Now the weight of 1 sheet is \[\dfrac{{40}}{{12}}grams\] .
We have to find a number of sheets that weigh \[16\dfrac{2}{3}\] kilogram.
First convert kilogram to gram.
\[ \Rightarrow 16\dfrac{2}{3}kg = \dfrac{{50}}{3}kg = \dfrac{{50 \times 1000}}{3}grams\]
Don’t calculate the numbers here only we will do it at last.
Now let’s find the number of sheets.
\[
   \Rightarrow 1sheet \to \dfrac{{40}}{{12}}grams \\
  ?sheets \to \dfrac{{50 \times 1000}}{3}grams \\
\]
\[ \Rightarrow ?sheets = \dfrac{{\dfrac{{50 \times 1000}}{3}}}{{\dfrac{{40}}{{12}}}} = \dfrac{{50 \times 1000 \times 12}}{{3 \times 40}}\]
Now divide 12 by 3
\[ \Rightarrow sheets = \dfrac{{50 \times 1000 \times 4}}{{40}}\]
Next divide 40 by 4 will give
\[ \Rightarrow sheets = \dfrac{{50 \times 1000}}{{10}}\]
Divide 1000 by 10 and it is equal to
\[
   \Rightarrow sheets = 50 \times 1000 \\
   \Rightarrow sheets = 50000 \\
\]
Thus the number of sheets required is \[50000\].

Note: Here student should focus on units of weight given. They are of weight measurement but are of different capacity so first make them either gram or kilogram. If this step is missed then the answer that a student will conclude will be totally wrong.