Question

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. The remaining 2 swans are in the water. Find the total number of swans.
​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that total number of swans be x.

$\sf \: Number \: of \: swans \: playing \: on \: bank \: of \: pond = \dfrac{7}{2} \sqrt{x}$

$\sf \: Number \: of \: swans \: in \: water = 2$

So,

$\rm :\longmapsto\:\dfrac{7}{2} \sqrt{x} + 2 = x$

$\rm :\longmapsto\:7 \sqrt{x} + 4 = 2x$

$\rm :\longmapsto\:2x - 7 \sqrt{x} - 4 = 0$

$\rm :\longmapsto\:2 {( \sqrt{x}) }^{2} - 7 \sqrt{x} - 4 = 0$

$\rm :\longmapsto\:2 {( \sqrt{x}) }^{2} - 8 \sqrt{x} + \sqrt{x} - 4 = 0$

$\rm :\longmapsto\:2 \sqrt{x}( \sqrt{x} - 4) + 1( \sqrt{x} - 4) = 0$

$\rm :\longmapsto\:( \sqrt{x} - 4)(2 \sqrt{x} + 1) = 0$

$\rm :\longmapsto\: \sqrt{x} = 4 \: \: \: or \: \: \: \sqrt{x} = - \dfrac{1}{2} \: \: \{rejected \}$

$\rm :\longmapsto\: \sqrt{x} = 4$

$\bf\implies \:x = 16$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf{Number \: of \: swans = 16}}}$

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.