Question 1029401
Let {{{ n }}} = number of items she bought
{{{ 120 / n - 16 = 120/( n + 24 ) }}}
Multiply both sides by {{{ n*( n + 24 ) }}}
{{{ 120*( n + 24 ) - 16*n*( n + 24 ) = 120n }}}
{{{ 120n + 2880 - 16n^2 - 384n = 120n }}}
{{{ 16n^2 + 384n - 2880 = 0 }}}
{{{ n^2 + 24n - 180 = 0 }}}
I can complete the square
{{{ n^2 + 24n = 180 }}}
{{{ n^2 + 24n + (24/2)^2 = 180 + (24/2)^2 }}}
{{{ n^2 + 24n + 144 = 180 + 144 }}}
{{{ ( n + 12 )^2 = 324 }}}
{{{ ( n + 12 )^2 = 18^2 }}}
{{{ n + 12 = 18 }}}
{{{ n = 6 }}}
She bought 6 items
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check:
{{{ 120 / n - 16 = 120/( n + 24 ) }}}
{{{ 120 / 6 - 16 = 120/( 6 + 24 ) }}}
{{{ 20 - 16 = 120/30 }}}
{{{ 4 = 4 }}}
OK