Question

A bag contains a number of balls out of which 1/4th are black in colour. 1/9 along with 1/4 are red. 7 times the square root of the total number are blue balls and the rest of 56 balls are white. Find the total number of balls there are in the bag.

Answer 1

Answer:  There are 36 balls in the bag.

Step-by-step explanation:

Since we have given that

Number of white balls = 56

Let the total number of balls be 'x'.

Number of black balls be $\frac{1}{4}x$

Number of red balls be

$\frac{x}{4}+\frac{x}{9}\\\\=\frac{13}{36}$

Number of blue balls be

$7\sqrt{x}$

Total number of black, red and blue balls is given by

$\frac{x}{4}+\frac{13x}{36}+7\sqrt{x}\\\\=\frac{22x}{36}+7\sqrt{x}\\\\=\frac{11x}{18}+7\sqrt{x}$

So, According to question,

$x-(\frac{11x}{18}+7\sqrt{x})=56\\\\x-\frac{11x}{18}-7\sqrt{x}=56\\\\\frac{7x}{18}-7\sqrt{x}=56\\\\\frac{x}{18}+\sqrt{x}=8\\\\Let\ \sqrt{x}=y\\\\y^2=x\\\\\text{So, it becomes}\\\\\frac{y^2}{18}+y=8\\\\y^2+18y-144=0\\\\y^2+24y-6y-144=0\\\\y(y+24)-6(y+24)\\\\y=-24,6$

Let y = 6

x=6² = 36.

Hence, there are 36 balls in the bag.