document.write( "Question 574467: At a thearer, 400 tickets were sold. The ticket prices were $8, $10, and $12. The total income from ticket sales was $3700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was seven times the number of $12 tickets sold. \n" ); document.write( "

Algebra.Com's Answer #369095 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = number of $8 tickets
\n" ); document.write( "Let $\"b\"$ = number of $10 tickets
\n" ); document.write( "Let $\"+c\"$ = number of $12 tickets
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+400+\"$
\n" ); document.write( "(2) $\"+8a+%2B+10b+%2B+12c+=+3700+\"$
\n" ); document.write( "(3) $\"+a+%2B+b+=+7c+\"$
\n" ); document.write( "--------------
\n" ); document.write( "This is 3 equations and 3 unknowns, so
\n" ); document.write( "it should be solvable
\n" ); document.write( "Substitute (3) into (1)
\n" ); document.write( "(1) $\"+7c+%2B+c+=+400+\"$
\n" ); document.write( "(1) $\"+8c+=+400+\"$
\n" ); document.write( "(1) $\"+c+=+50+\"$
\n" ); document.write( "Plug this value into (2)
\n" ); document.write( "(2) $\"+8a+%2B+10b+%2B+12%2A50+=+3700+\"$
\n" ); document.write( "(2) $\"+8a+%2B+10b+%2B+600+=+3700+\"$
\n" ); document.write( "(2) $\"+8a+%2B+10b+=+3100+\"$
\n" ); document.write( "(2) $\"+4a+%2B+5b+=+1550+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+400+\"$
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+50+=+400+\"$
\n" ); document.write( "(1) $\"+a+%2B+b+=+350+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+4+\"$
\n" ); document.write( "(1) $\"+4a+%2B+4b+=+1400+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+4a+%2B+5b+=+1550+\"$
\n" ); document.write( "(1) $\"+-4a+-+4b+=+-1400+\"$
\n" ); document.write( " $\"+b+=+150+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(3) $\"+a+%2B+b+=+7c+\"$
\n" ); document.write( "(3) $\"+a+%2B+150+=+7%2A50+\"$
\n" ); document.write( "(3) $\"+a+=+350+-+150+\"$
\n" ); document.write( "(3) $\"+a+=+200+\"$
\n" ); document.write( "There are 200 $8 tickets
\n" ); document.write( "There are 150 $10 tickets
\n" ); document.write( "There are 50 $12 tickets
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+8%2A200+%2B+10%2A150+%2B+12%2A50+=+3700+\"$
\n" ); document.write( "(2) $\"+1600+%2B+1500+%2B+600+=+3700+\"$
\n" ); document.write( "(2) $\"+3700+=+3700+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );