document.write( "Question 1029401: A woman bought a number of items for $120. She realized if she had bought 24 more items for the same money, she would have paid 16 less per item. How many items did she buy? \n" ); document.write( "

Algebra.Com's Answer #644496 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = number of items she bought
\n" ); document.write( " $\"+120+%2F+n+-+16+=+120%2F%28+n+%2B+24+%29+\"$
\n" ); document.write( "Multiply both sides by $\"+n%2A%28+n+%2B+24+%29+\"$
\n" ); document.write( " $\"+120%2A%28+n+%2B+24+%29+-+16%2An%2A%28+n+%2B+24+%29+=+120n+\"$
\n" ); document.write( " $\"+120n+%2B+2880+-+16n%5E2+-+384n+=+120n+\"$
\n" ); document.write( " $\"+16n%5E2+%2B+384n+-+2880+=+0+\"$
\n" ); document.write( " $\"+n%5E2+%2B+24n+-+180+=+0+\"$
\n" ); document.write( "I can complete the square
\n" ); document.write( " $\"+n%5E2+%2B+24n+=+180+\"$
\n" ); document.write( " $\"+n%5E2+%2B+24n+%2B+%2824%2F2%29%5E2+=+180+%2B+%2824%2F2%29%5E2+\"$
\n" ); document.write( " $\"+n%5E2+%2B+24n+%2B+144+=+180+%2B+144+\"$
\n" ); document.write( " $\"+%28+n+%2B+12+%29%5E2+=+324+\"$
\n" ); document.write( " $\"+%28+n+%2B+12+%29%5E2+=+18%5E2+\"$
\n" ); document.write( " $\"+n+%2B+12+=+18+\"$
\n" ); document.write( " $\"+n+=+6+\"$
\n" ); document.write( "She bought 6 items
\n" ); document.write( "-------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+120+%2F+n+-+16+=+120%2F%28+n+%2B+24+%29+\"$
\n" ); document.write( " $\"+120+%2F+6+-+16+=+120%2F%28+6+%2B+24+%29+\"$
\n" ); document.write( " $\"+20+-+16+=+120%2F30+\"$
\n" ); document.write( " $\"+4+=+4+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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