Question

One-fourth of a herd of camels was seen in a forest. Twice the square root of the herd had gone to the mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.

Answer 1

Hint: Get an equation by finding the sum of all the fractions given in the question and then equate it with the total number of camels in the herd you have assumed. Solve the equation to get and answer.

Complete step by step answer:
Let the total number of camels in the herd be x.
Now number of camels seen the forest is \[ = \dfrac{1}{4}x = \dfrac{x}{4}\]
Number of camels gone to the mountains \[ = 2\sqrt x \]
Number of camels seen on the river bank \[ = 15\]
Now the total number of camels in the herd \[ = \dfrac{x}{4} + 2\sqrt x + 15\]
We have also assumed that the total number of camels is x
Therefore equating both we get the equation
\[ \Rightarrow \dfrac{x}{4} + 2\sqrt x + 15 = x\]
Now let us try to solve this equation to get the value of x.
\[\begin{array}{l}
 \Rightarrow \dfrac{x}{4} + 2\sqrt x + 15 = x\\
 \Rightarrow 2\sqrt x = x - \dfrac{x}{4} - 15\\
 \Rightarrow 2\sqrt x = \dfrac{{3x}}{4} - 15
\end{array}\]
By squaring both sides we get it as
\[\begin{array}{l}
 \Rightarrow {\left( {2\sqrt x } \right)^2} = {\left( {\dfrac{{3x}}{4} - 15} \right)^2}\\
 \Rightarrow 4x = \dfrac{{9{x^2}}}{{16}} - \dfrac{{45x}}{2} + 225\\
 \Rightarrow \dfrac{{9{x^2}}}{{16}} - \dfrac{{45x}}{2} - 4x + 225 = 0\\
 \Rightarrow \dfrac{{9{x^2} - 424x + 3600}}{{16}} = 0\\
 \Rightarrow 9{x^2} - 424x + 3600 = 0\\
 \Rightarrow 9{x^2} - 324x - 100x + 3600 = 0\\
 \Rightarrow 9x(x - 36) - 100(x - 36) = 0\\
 \Rightarrow (9x - 100)(x - 36) = 0\\
 \Rightarrow x = 36,\dfrac{{100}}{9}
\end{array}\]
We are not taking the value \[\dfrac{{100}}{9}\] because number of camels cannot be in fraction
Therefore the number of camels in the herd are 36

Note: I have used the algebraic formula \[{(a - b)^2} = {a^2} - 2ab + {b^2}\] While opening the brackets in the right hand side after squaring both the sides. Also \[{\left( {\sqrt x } \right)^2} = x\] because \[{\left( {{x^{\dfrac{1}{2}}}} \right)^2} = {x^{\dfrac{1}{2} \times 2}} = x\] .