document.write( "Question 162558: a basketball team sells tickets that cost $10 $20 or VIP seats, $30. The team has sold 492 tickets over all. It has sold 177 more $20 tickets than $10 tickets. The total sales are $8580. How Many tickets of each kind have been sold? \n" ); document.write( "
Algebra.Com's Answer #119824 by ankor@dixie-net.com(22740)\"\" \"About 
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A basketball team sells tickets that cost $10 $20 or VIP seats, $30.
\n" ); document.write( "The no. of three types of tickets = x, y, z
\n" ); document.write( ";
\n" ); document.write( "The team has sold 492 tickets over all.
\n" ); document.write( "x + y + z = 492
\n" ); document.write( ":
\n" ); document.write( "It has sold 177 more $20 tickets than $10 tickets.
\n" ); document.write( "y = x + 177
\n" ); document.write( ":
\n" ); document.write( "The total sales are $8580.
\n" ); document.write( "10x + 20y + 30z = 8580
\n" ); document.write( ":
\n" ); document.write( "How Many tickets of each kind have been sold?
\n" ); document.write( ":
\n" ); document.write( "Replace (x+177) for y in the 1st and 3rd equations
\n" ); document.write( "x + (177+x) + z = 492
\n" ); document.write( "2x + z = 492 - 177
\n" ); document.write( "2x + z = 315
\n" ); document.write( "and
\n" ); document.write( "10x + 20(x+177) + 30z = 8580
\n" ); document.write( "10x + 20x + 3540 + 30z = 8580
\n" ); document.write( "30x + 30z = 8580 - 3540
\n" ); document.write( "30x + 30z = 5040
\n" ); document.write( "Simplify, divide equation by 30
\n" ); document.write( "x + z = 168
\n" ); document.write( ":
\n" ); document.write( "Using these two equations for elimination
\n" ); document.write( "2x + z = 315
\n" ); document.write( "x + z = 168
\n" ); document.write( "---------------subtracting eliminates z
\n" ); document.write( "x = 147 ea $10 tickets sold
\n" ); document.write( ":
\n" ); document.write( "y = 147 + 177
\n" ); document.write( "y = 324 ea $20 tickets sold
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\n" ); document.write( "Find z using the 1st equation
\n" ); document.write( "147 + 324 + z = 492
\n" ); document.write( "471 + z = 492
\n" ); document.write( "z = 492 - 471
\n" ); document.write( "z = 21 ea $30 tickets sold
\n" ); document.write( ":
\n" ); document.write( "Check solution in the $$ equation
\n" ); document.write( "10(147) + 20(324) + 30(21) =
\n" ); document.write( "1470 + 6480 + 630 = 8580; confirms our solutions \n" ); document.write( "
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