Question

the sum of my nieces and nephews equals 15,and theri product equals 54,and i have more nephews than nieces ,how many nephews and how many nicecs is this book dedicated to?

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{x=6\:and\:y=9 \:OR\:x=9\:and\:y=6}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

$Let\:nieces\: be \:= \:x\\</p><p> nephews\:be\:= \ :y$

To find :

$number\:of\:nieces\:=?\\number \: of\:nephews\:=?\\>>According\: to\: the \: given\:question:$

$x + y = 15 - - - - - (1) \\ x \times y = 54 \\ = ) y = \frac{54}{x} - - - - - (2) \\ \\ > > putting \: value \: of \: y \: in \: (1) \\ x + \frac{54}{ x } = 15 \\ = ) \frac{ {x}^{2} + 54 }{x} = 15 \\ = ) {x}^{2} + 54 = 15x \\ = ) {x}^{2} - 15x + 54 =0 \\ = ) {x}^{2} - 9x - 6x + 54 = 0 \\ = )x(x - 9) - 6(x - 9) = 0 \\ = )(x - 6)(x - 9) = 0 \\ \\ x - 6 = 0 \\ x = 6 - - - - - 1st \: value \\ x - 9 = 0 \\ x = 9 - - - - - 2nd \: value \\\\ first \: put \: the \: value \: of \: x = 6 \: then \\ x + y = 15 \\ 6 + y = 15 \\ y = 15 - 6 \\ y= 9 \\\\ if \: we \: put \: value \: of \: x = 9 \: then \\ x + y = 15 \\ 9 + y = 15 \\ y= 6$

$\huge{\boxed{\boxed{\sf{x=6\:and\:y=9 \:OR\:x=9\:and\:y=6}}}}$

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