Question 1077404
Let {{{ n }}} = the number of items she bought
{{{ 24/n }}} = the cost she paid per item
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If she bought {{{ n+3 }}} items for $24, the cost per item
would have been {{{ 24/n - 4 }}}
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I can say:
{{{ 24/( n+3 ) = 24/n - 4 }}}
Multiply both sides by {{{ n*( n+3 ) }}}
{{{ 24n = 24*( n+3 ) - 4*n*( n+3 ) }}}
{{{ 24n = 24n + 72 - 4n^2 - 12n }}}
{{{ 4n^2 + 12n - 72 = 0 }}}
{{{ n^2 + 3n - 18 = 0 }}}
{{{ ( n + 6 )*( n - 3 ) = 0 }}} ( by looking at it )
{{{ n = 3 }}} ( can't use the negative solution )
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She bough 3 items
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check:
3 items for $24 is $8 per item
If she bought 3 more, or 6 items for $24, the
cost per item is $4, and this is $4 less than
the $8 per item actually paid.
OK