Question

There are x boys playing in the park. The number of girls in the park is equal to the square root of the number of boys. If the total number of boys and girls playing in the park is 42, find the number of boys.​

Answer 1

Number of boys in the park is 36

Explanation:

Number of boys playing = x

Number of girls playing in park =
`√(x)`

Total children playing in the park = 42

Now, accoding to the question,

Number of Boys + Number of girls = Total children in park

`x + √(x)   = 42`

or,
`√(x)   = 42 - x`

Squaring both sides we get

`x =  1764 +  x^(2)   - 84x`

or,
`x^(2)   - 85x    + 1764  = 0`

or,
`x^(2)   - 49x -36x    + 1764  = 0`

⇒(x-49)(x-36) = 0

⇒ either x = 49, or x = 36

if number of boys playing in the park is 49,

then number of girls = 42 -49 NOT POSSIBLE

⇒ x ≠ 49

Hence, x = 36 = Number of boys

And, Number of girls = 42 - 36 = 6