Question 925610

if the total number of children is {{{x}}}

{{{(5/2)sqrt(x)}}}   play football

{{{(1/4)x}}}  play tennis 

 the remaining {{{28}}} children play basketball

so, {{{x=(5/2)sqrt(x)+(1/4)x+28}}} ....solve for {{{x}}}, both sides multiply by {{{4}}}

{{{4x=4(5/2)sqrt(x)+4(1/4)x+28*4}}}

{{{4x=10sqrt(x)+x+112}}}

{{{3x-112=10sqrt(x)}}}....square both sides

{{{(3x-112)^2=(10sqrt(x))^2}}}

{{{9x^2-672x+12544=100x}}}

{{{9x^2-672x-100x+12544=0}}}

{{{9x^2-772x+12544=0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{x = (-(-772) +- sqrt( (-772)^2-4*9*12544 ))/(2*9) }}} 


{{{x = (772 +- sqrt( 595984-451584 ))/18 }}} 


{{{x = (772 +- sqrt( 144400 ))/18 }}} 


{{{x = (772 +- 380)/18 }}} 

solutions:

{{{x = (772 +380)/18 }}} 

{{{x = 1152/18 }}} 

{{{x = 64}}} 

or

{{{x = (772 -380)/18 }}} 

{{{x = 392/18 }}} 

{{{x = 21.78 }}} ...we can not use decimal for number of the children


=> our solution is {{{highlight(x = 64 )}}}

check:
so, if the total number of children is {{{64}}}

{{{(5/2)sqrt(64)=(5/2)*8=5*4=20}}}   play football

{{{(1/4)64=64/4=16}}}  play tennis 

 the remaining {{{64-(20+16)=64-36=28}}} children play basketball