document.write( "Question 725854: Tickets for a high school dance cost $1.00 each if purchased in advance of the dance, but $1.50 each if bought at the door. If 100 tickets were sold and $120 was collected, how many tickets were sold in advance and how many we're sold at the door? \n" ); document.write( "

Algebra.Com's Answer #444355 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of tickets sold in advance
\n" ); document.write( "Let $\"+b+\"$ = number sold at the door
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(2) $\"+1%2Aa+%2B+1.5%2Ab+=+120+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(2) $\"+10a+%2B+15b+=+1200+\"$
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+240+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+240+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-200+\"$
\n" ); document.write( " $\"+b+=+40+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(1) $\"+a+%2B+40+=+100+\"$
\n" ); document.write( "(1) $\"+a+=+60+\"$
\n" ); document.write( "60 tickets were sold in advance
\n" ); document.write( "40 tickets were sold at the door
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+1%2Aa+%2B+1.5%2Ab+=+120+\"$
\n" ); document.write( "(2) $\"+1%2A60+%2B+1.5%2A40+=+120+\"$
\n" ); document.write( "(2) $\"+60+%2B+60+=+120+\"$
\n" ); document.write( "(2) $\"+120+=+120+\"$
\n" ); document.write( "OK \n" ); document.write( "

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