document.write( "Question 161845: adult tickets for the school musical sold for $3.50 and student tickets sikd fir $2.50. Three hundred twenty one tickets were sold altogether for $937.50 How many of each kind of ticket were sold?\r \n" );
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document.write( "Notice that in problems like this you have to consider two things: \n" );
document.write( "prices \n" );
document.write( "quantity of tickets sold \n" );
document.write( "You cannot combine them in only one equation because they represent different things; so you will need two equations. \n" );
document.write( "Now before we construct the two equations; lets set up our variables\r \n" );
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document.write( "Let a represent adult tickets \n" );
document.write( "Let s represent student tickets\r \n" );
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document.write( "Now lets look at what we now about these two when thinking about them in money terms:\r \n" );
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document.write( "$3.50 per adult \n" );
document.write( "$2.50 per student \n" );
document.write( "Total made $937.50\r \n" );
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document.write( "Lets show it algebraically: 3.50a + 2.50s=$937.50\r \n" );
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document.write( "When thinking about the tickets in numbers we now the number sold were 321 so algebraically a + s = 321\r \n" );
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document.write( "Two equations; two variables; we can solve...........\r \n" );
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document.write( "a + s = 321 ....... which is the same as.... s= 321 - a \n" );
document.write( "3.50a + 2.50s = 937.50\r \n" );
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document.write( "Since s = 321-a, we can substitute this into second equation:\r \n" );
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document.write( "3.50a + 2.50(321-a)=937.50 \n" );
document.write( "3.50a+802.5-2.50a=937.50 \n" );
document.write( "3.50a-2.50a+802.5=937.50 \n" );
document.write( "1.00a+802.5=937.50 \n" );
document.write( "a=135\r \n" );
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document.write( "Then s=321-135 \n" );
document.write( "s=186\r \n" );
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document.write( "Check: \n" );
document.write( "a+s=135+186=321 check \n" );
document.write( "3.50a+2.50s=3.50(135)+2.50(186)=472.50+465=937.50 check\r \n" );
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