Question

Each student participating in a mass drill requires $2\dfrac{2}{5}m$ of ribbon. If the total length of ribbon is 240m how many students participated in the drill?

Answer 1

Hint: Let us take x number of students participated in mass drill. Hence we have the total length of ribbon is $2\dfrac{2}{5}\times x$ . Now we know that the total length is 240m hence we will form a linear equation and solve to find the value of x.

Complete step by step answer:
Now we are given that each student that participates in mass drill requires $2\dfrac{2}{5}m$ of ribbon.
Let us first simplify the above fraction. Now we know that $2\dfrac{2}{5}m$ is nothing but $2+\dfrac{2}{5}$
Hence we can also write it as $\dfrac{2}{1}+\dfrac{2}{5}$ Since $\dfrac{2}{1}=2$ .
Now taking LCM of 1 and 5 we get
$2\dfrac{2}{5}=\dfrac{10+2}{5}=\dfrac{12}{5}$
Hence we get $2\dfrac{2}{5}m=\dfrac{12}{5}m$ .
Hence each student requires $\dfrac{12}{5}m$ length of ribbon..
Now let us consider there are x number of students in drill.
Now if each student requires $\dfrac{12}{5}m$ length of ribbon,
Then the x number of students will require $\left( \dfrac{12}{5}\times x \right)m$ length of ribbon.
Hence we get x number of students requiring $\left( \dfrac{12}{5}\times x \right)m$ length of ribbon.
Now we are given that the total length ribbon is 240m.
Hence we get the equation
$\left( \dfrac{12}{5}\times x \right)=240$
Now multiplying the above equation by 5 we get
$12x=240\times 5$
Now dividing the above equation by 12 we get
$\begin{align}
  & x=20\times 5 \\
 & \Rightarrow x=100 \\
\end{align}$

Hence we get total number of students who participated in the drill is 100.

Note: Note that when we write $2\dfrac{1}{3}$ it means \[2+\dfrac{1}{3}\] and not $2\times \dfrac{1}{3}$ . Hence we have \[2\dfrac{1}{3}=\dfrac{7}{3}\] and $2\dfrac{1}{3}\ne \dfrac{2}{3}$ . Hence in short to calculate $a\dfrac{p}{q}$ we can directly write it as $\dfrac{aq+p}{q}$ and also when we have $\left( \dfrac{12}{5}\times x \right)=240$ we can directly take $\dfrac{12}{5}$ to RHS. And get $x=240\times \dfrac{5}{12}$ since it is in multiplication the fraction gets inverted.