Q. 11. From a group of swans,7/2
times the square root of their total number are playing on the bank of a
pond. Th

1 thought on “<br />Q. 11. From a group of swans,7/2<br />times the square root of their total number are playing on the bank of a<br />pond. Th”

1. [tex]\large\underline{\sf{Solution-}}[/tex]

   Let assume that total number of swans be x.

   [tex] \sf \: Number \: of \: swans \: playing \: on \: bank \: of \: pond = \dfrac{7}{2} \sqrt{x} [/tex]

   [tex] \sf \: Number \: of \: swans \: in \: water = 2[/tex]

   So,

   [tex]\rm :\longmapsto\:\dfrac{7}{2} \sqrt{x} + 2 = x[/tex]

   [tex]\rm :\longmapsto\:7 \sqrt{x} + 4 = 2x [/tex]

   [tex]\rm :\longmapsto\:2x – 7 \sqrt{x} – 4 = 0[/tex]

   [tex]\rm :\longmapsto\:2 {( \sqrt{x}) }^{2} – 7 \sqrt{x} – 4 = 0[/tex]

   [tex]\rm :\longmapsto\:2 {( \sqrt{x}) }^{2} – 8 \sqrt{x} + \sqrt{x} – 4 = 0[/tex]

   [tex]\rm :\longmapsto\:2 \sqrt{x}( \sqrt{x} – 4) + 1( \sqrt{x} – 4) = 0 [/tex]

   [tex]\rm :\longmapsto\:( \sqrt{x} – 4)(2 \sqrt{x} + 1) = 0[/tex]

   [tex]\rm :\longmapsto\: \sqrt{x} = 4 \: \: \: or \: \: \: \sqrt{x} = – \dfrac{1}{2} \: \: \{rejected \}[/tex]

   [tex]\rm :\longmapsto\: \sqrt{x} = 4[/tex]

   [tex]\bf\implies \:x = 16[/tex]

   [tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf{Number \: of \: swans = 16}}}[/tex]

   Basic Concept Used :-

   Writing System of Equation from Word Problem.

   1. Understand the problem.

   • Understand all the words used in stating the problem.

   • Understand what you are asked to find.

   2. Translate the problem to an equation.

   • Assign a variable (or variables) to represent the unknown.

   • Clearly state what the variable represents.

   3. Carry out the plan and solve the problem.

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