document.write( "Question 119997This question is from textbook Beginning and intermediate Algebra
\n" ); document.write( ": 29. A bookstore can purchase several calculators for a total cost of $120. If each calculator cost $1 less, the bookstore could purchase 10 additional calculators at the same total cost. How many calculators can be purchased at the regular price? \n" ); document.write( "

Algebra.Com's Answer #87960 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"c\"$ = the cost of each calculator
\n" ); document.write( "Let $\"n\"$ = number of calculators bought
\n" ); document.write( "In words:
\n" ); document.write( "Total cost = ( cost of each calculator ) x ( number of calculators bought )
\n" ); document.write( " $\"120+=+c%2An\"$
\n" ); document.write( " $\"c+=+120%2Fn\"$
\n" ); document.write( "also given is
\n" ); document.write( " $\"120+=+%28c-1%29%2An+%2B+10%28c-1%29\"$
\n" ); document.write( " $\"120+=+%28c-1%29%28n%2B10%29\"$
\n" ); document.write( "Substitute $\"120%2Fn\"$ for $\"c\"$
\n" ); document.write( " $\"120+=+%28120%2Fn+-+1%29%28n+%2B+10%29\"$
\n" ); document.write( " $\"120+=+%28%28120-n%29%2Fn%29%2810%2Bn%29\"$
\n" ); document.write( " $\"120n+=+1200+-+10n+%2B+120n+-+n%5E2\"$
\n" ); document.write( " $\"n%5E2+%2B+10n+=+1200\"$
\n" ); document.write( "complete the square
\n" ); document.write( " $\"n%5E2+%2B+10n+%2B+25+=+1225\"$
\n" ); document.write( " $\"%28n%2B5%29%5E2+=+1225\"$
\n" ); document.write( " $\"n+%2B+5+=+35\"$
\n" ); document.write( " $\"n+=+30\"$
\n" ); document.write( "Thirty calculators can be bought at the regular price answer
\n" ); document.write( "check:
\n" ); document.write( " $\"120+=+%28c-1%29%2An+%2B+10%28c-1%29\"$
\n" ); document.write( " $\"120+=+%28c-1%29%2A30+%2B+10%28c-1%29\"$
\n" ); document.write( " $\"120+=+%28c-1%29%2A40\"$
\n" ); document.write( " $\"c-1+=+3\"$
\n" ); document.write( " $\"c+=+4\"$
\n" ); document.write( "This says the regular price is $4
\n" ); document.write( " $\"120+=+c%2An\"$
\n" ); document.write( " $\"120+=+30%2A4\"$
\n" ); document.write( " $\"120+=+120\"$
\n" ); document.write( "OK
\n" ); document.write( "
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