Question

Out of a group of students,49/5 times the square root of the total numbers are playing cricket. Remaining 2 are idle find the total number of students

Answer 1

Answer:

Step-by-step explanation:

Our aim is to answer the following question: out of a group of students,49/5 times the square root of the total numbers are playing cricket. Remaining 2 are idle find the total number of students.

Lets consider x^2 the total number of ducks.

We know that from the x^2 students 49/5 times the square root of the total number are playing cricket. Thus 49/5 * $\sqrt{x^{2} }$ = 49x/5.

Also the number of students idle is 2.

Hence we can say that the total number of students is equal to the number of students idle and the number of students that are playing cricket. that is,

x^2 = 49x/5 + 2

Using the quadratic equation we get x = 0.2085183577 and x = 9.591481642 as solutions.

Since 0.2 is not possible to consider as a number of people we have x = 9.591481642.

Hence, the total number of  students is x^2 = 9.591481642^2 = 91.99652009, this is approximately equal to 92 students.

I hope this helps you!

Keep up with the good studies!!

Answer 2

The total number of students is 100

Solution:

Let "x" be the total number of students

Given,

49/5 times the square root of the total numbers are playing cricket

Remaining 2 are idle

Therefore, we frame a equation as:

$\frac{49}{5} \times \sqrt{x} + 2 = x\\\\49\sqrt{x}+10= 5x \\\\49\sqrt{x} = 5x - 10\\\\\mathrm{Square\:both\:sides}\\\\2401 x = (5x - 10)^2 \\\\2401x=25x^2-100x+100\\\\25x^2-2501x+100=0$

$Break\:the\:expression\:into\:groups\\\\\left(25x^2-x\right)+\left(-2500x+100\right) = 0\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}25x^2-x\\\\\mathrm{Factor\:out\:}-100\mathrm{\:from\:}-2500x+100\\\\x\left(25x-1\right)-100\left(25x-1\right) = 0\\\\\mathrm{Factor\:out\:common\:term\:}25x-1\\\\\left(25x-1\right)\left(x-100\right) = 0\\\\Thus\\\\25x = 1\\\\x = \frac{1}{25}\ ignore\ as\ number\ of\ students\ cant\ be\ fraction$

$x - 100 = 0\\\\x = 100$

Thus, total number of students is 100

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