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Answers
Answer:
\begin{gathered} \boxed{ \bf{ \:Number \: of \:students \: = \: 72 \: }} \\ \\ \end{gathered}
Numberofstudents=72
Step-by-step explanation:
Let assume that number of students went on the picnic be x.
It is given that, half of the students were playing in the ground.
\begin{gathered}\implies\sf \: Number\:of\:students\:playing\:in\:ground = \dfrac{x}{2} \\ \\ \end{gathered}
⟹Numberofstudentsplayinginground=
2
x
So,
\begin{gathered}\implies\sf \:Remaining \: number\:of\:students = x - \dfrac{x}{2} = \dfrac{x}{2} \\ \\ \end{gathered}
⟹Remainingnumberofstudents=x−
2
x
=
2
x
Further given that, Three-fourth of the rest were cooking food.
\begin{gathered}\implies\sf \: Number\:of\:students\:cooking\:food = \dfrac{3}{4} \times \dfrac{x}{2} = \dfrac{3x}{8} \\ \\ \end{gathered}
⟹Numberofstudentscookingfood=
4
3
×
2
x
=
8
3x
Further, given that, 9 students were making tent.
So,
\begin{gathered}\sf \: \dfrac{x}{2} + \dfrac{3x}{8} + 9 = x \\ \\ \end{gathered}
2
x
+
8
3x
+9=x
\begin{gathered}\sf \: \dfrac{4x + 3x + 72}{8} = x \\ \\ \end{gathered}
8
4x+3x+72
=x
\begin{gathered}\sf \: \dfrac{7x + 72}{8} = x \\ \\ \end{gathered}
8
7x+72
=x
\begin{gathered}\sf \: 7x + 72 = 8x \\ \\ \end{gathered}
7x+72=8x
\begin{gathered}\sf \: 8x - 7x = 72 \\ \\ \end{gathered}
8x−7x=72
\begin{gathered}\implies\sf \: x = 72 \\ \\ \end{gathered}
⟹x=72
Hence,
\begin{gathered}\sf\implies \boxed{ \sf{ \:Number \: of \:students\: = \:72\: }} \\ \\ \end{gathered}
⟹
Numberofstudents=72