Question 536713
Let {{{ n }}} = the number of tennis balls she bought
Her cost/ball is {{{ 600/n }}}
The cost/ball minus 25 cents is {{{ 600/n - .25 }}}
given:
( cost/ball ) x ( number of balls ) = cost
{{{ ( 600/n - .25 )*( n + 10 ) = 600 }}}
-----------------------------
{{{ 600 - .25n + 6000/n - 2.5 = 600 }}}
Subtract {{{600}}} from both sides
{{{ -.25n + 6000/n - 2.5 = 0 }}}
{{{ -.25n + 6000/n = 2.5 }}}
Multiply both sides by {{{n}}}
{{{ -.25n^2 + 6000 = 2.5n }}}
{{{ -.25n^2 - 2.5n + 6000 = 0 }}}
Multiply both sides by {{{ 4 }}}
{{{ -n^2 -10n + 24000 = 0 }}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -1 }}}
{{{ b = -10 }}}
{{{ c = 24000 }}}
{{{ n = (-(-10) +- sqrt( (-10)^2-4*(-1)*24000 ))/(2*(-1)) }}}
{{{ n = ( 10 +- sqrt(  100 + 96000 ))/(-2) }}}
{{{ n = ( 10 - 310)/(-2) }}} ( use the (-) square root )
{{{ n = -300/-2 }}} 
{{{ n = 150 }}}
She paid $600 for 150 balls, so she paid
{{{ 600 / 150 = 4 }}}
$4 for each ball
check answer:
{{{ ( 600/n - .25 )*( n + 10 ) = 600 }}}
{{{ ( 600/150 - .25 )*( 150 + 10 ) = 600 }}}
{{{ ( 4 - .25 )*160 = 600 }}}
{{{ 3.75*160 = 600 }}}
{{{ 600 = 600 }}}
OK