document.write( "Question 1077404: A woman bought a number of items for $24. She realized that if she had bought 3 more items for the same money, she would have paid $4 less per item. How many items did she buy? \n" ); document.write( "

Algebra.Com's Answer #691864 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = the number of items she bought
\n" ); document.write( " $\"+24%2Fn+\"$ = the cost she paid per item
\n" ); document.write( "-------------------------------------------
\n" ); document.write( "If she bought $\"+n%2B3+\"$ items for $24, the cost per item
\n" ); document.write( "would have been $\"+24%2Fn+-+4+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "I can say:
\n" ); document.write( " $\"+24%2F%28+n%2B3+%29+=+24%2Fn+-+4+\"$
\n" ); document.write( "Multiply both sides by $\"+n%2A%28+n%2B3+%29+\"$
\n" ); document.write( " $\"+24n+=+24%2A%28+n%2B3+%29+-+4%2An%2A%28+n%2B3+%29+\"$
\n" ); document.write( " $\"+24n+=+24n+%2B+72+-+4n%5E2+-+12n+\"$
\n" ); document.write( " $\"+4n%5E2+%2B+12n+-+72+=+0+\"$
\n" ); document.write( " $\"+n%5E2+%2B+3n+-+18+=+0+\"$
\n" ); document.write( " $\"+%28+n+%2B+6+%29%2A%28+n+-+3+%29+=+0+\"$ ( by looking at it )
\n" ); document.write( " $\"+n+=+3+\"$ ( can't use the negative solution )
\n" ); document.write( "-------------------------
\n" ); document.write( "She bough 3 items
\n" ); document.write( "----------------------
\n" ); document.write( "check:
\n" ); document.write( "3 items for $24 is $8 per item
\n" ); document.write( "If she bought 3 more, or 6 items for $24, the
\n" ); document.write( "cost per item is $4, and this is $4 less than
\n" ); document.write( "the $8 per item actually paid.
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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