document.write( "Question 220641: Sammy spends 10 Euros on some cans of drink. In another shop she sees that the same cans are each 10 cents cheaper, and she calculates that she could have brought 5 more cans for the same money. How many cans did she buy? \n" ); document.write( "

Algebra.Com's Answer #165604 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"x\"$ = number of cans bought
\n" ); document.write( "given:
\n" ); document.write( " $\"10%2Fx\"$ = price per can in euros
\n" ); document.write( "In the other shop, price per can = $\"10%2Fx+-+.1\"$
\n" ); document.write( "The same money is $\"10\"$ euros, so
\n" ); document.write( " $\"10+=+%2810%2Fx+-+.1%29%2A%28x+%2B+5%29\"$
\n" ); document.write( " $\"10+=+10+-+.1x+%2B+50%2Fx+-+.5\"$
\n" ); document.write( " $\".5+=+50%2Fx+-+.1x\"$
\n" ); document.write( " $\".5x+=+50+-+.1x%5E2\"$
\n" ); document.write( " $\"5x+=+500+-+x%5E2\"$
\n" ); document.write( " $\"x%5E2+%2B+5x+-+500+=+0\"$
\n" ); document.write( "by quadratic equation:
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+5\"$
\n" ); document.write( " $\"c+=+-500\"$
\n" ); document.write( " $\"x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-500%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"x+=+%28-5+%2B-+sqrt%28+25+%2B+2000+%29%29%2F2+\"$
\n" ); document.write( " $\"x+=+%28-5+%2B-+45%29%2F2+\"$
\n" ); document.write( " $\"x+=+%28-5+%2B+45%29%2F2\"$
\n" ); document.write( " $\"x+=+20\"$ (reject the negative solution)
\n" ); document.write( "She bought 20 cans
\n" ); document.write( "check answer:
\n" ); document.write( " $\"10+=+%2810%2Fx+-+.1%29%2A%28x+%2B+5%29\"$
\n" ); document.write( " $\"10+=+%2810%2F20+-+.1%29%2A%2820+%2B+5%29\"$
\n" ); document.write( " $\"10+=+%28.5+-+.1%29%2A25\"$
\n" ); document.write( " $\"10+=+.4%2A25\"$
\n" ); document.write( " $\"10+=+10\"$
\n" ); document.write( "OK \n" ); document.write( "

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