document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171608>Question 1171608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word problems are my weakness, please help\r<BR>\n" );
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document.write( "Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $30. For one performance, there were 40 tickets sold in all, and the total amount paid for them was $1325. How many tickets of each type were sold? </SPAN>\n" );
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document.write( "x = number of advance tickets sold<BR>\n" );
document.write( "y = number of same-day tickets sold<BR>\n" );
document.write( "x and y are placeholders for nonnegative whole numbers\r<BR>\n" );
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document.write( "The first equation is x+y = 40 because the instructions state \"there were 40 tickets sold in all\". \r<BR>\n" );
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document.write( "Let's solve for y to get y = 40-x. I subtracted x from both sides.\r<BR>\n" );
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document.write( "1 advance ticket costs $35<BR>\n" );
document.write( "x advance tickets cost 35x dollars<BR>\n" );
document.write( "eg: if you sold x = 10 advance tickets then 35*x = 35*10 = 350 dollars is earned from these tickets alone\r<BR>\n" );
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document.write( "1 same-day ticket costs $30<BR>\n" );
document.write( "y of these tickets costs 30y dollars <BR>\n" );
document.write( "eg: if you sold y = 20 same-day tickets then 30*y = 30*20 = 600 dollars is earned from these tickets alone\r<BR>\n" );
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document.write( "In total we have 35x+30y dollars earned from both types of tickets combined.\r<BR>\n" );
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document.write( "We're told that \"The total amount paid for them was $1325\" so 35x+30y = 1325 is the second equation.\r<BR>\n" );
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document.write( "The system of equations we have is<BR>\n" );
document.write( "y = 40-x<BR>\n" );
document.write( "35x+30y = 1325\r<BR>\n" );
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document.write( "We can use substitution to solve<BR>\n" );
document.write( "35x+30y = 1325\r<BR>\n" );
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document.write( "35x+30( y ) = 1325\r<BR>\n" );
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document.write( "35x+30( 40-x ) = 1325  .... y replaced with 40-x\r<BR>\n" );
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document.write( "35x+30( 40 ) + 30( -x ) = 1325 \r<BR>\n" );
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document.write( "35x+1200-30x = 1325 \r<BR>\n" );
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document.write( "5x+1200 = 1325 \r<BR>\n" );
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document.write( "5x+1200-1200 = 1325-1200 .... subtract 1200 from both sides\r<BR>\n" );
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document.write( "5x = 125\r<BR>\n" );
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document.write( "5x/5 = 125/5 .... dividing both sides by 5\r<BR>\n" );
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document.write( "x = 25\r<BR>\n" );
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document.write( "There were 25 advance tickets sold.\r<BR>\n" );
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document.write( "Use this to find y<BR>\n" );
document.write( "y = 40-x\r<BR>\n" );
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document.write( "y = 40-25\r<BR>\n" );
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document.write( "y = 15\r<BR>\n" );
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document.write( "There were 15 same-day tickets sold.\r<BR>\n" );
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document.write( "As a check,<BR>\n" );
document.write( "x+y = 25+15 = 40<BR>\n" );
document.write( "helps show that 40 tickets were sold<BR>\n" );
document.write( "This confirms the first equation.\r<BR>\n" );
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document.write( "And also,<BR>\n" );
document.write( "35x = 35*25 = 875 dollars earned from advance tickets only<BR>\n" );
document.write( "30y = 30*15 = 450 dollars earned from same-day tickets only<BR>\n" );
document.write( "35x+30y = 875+450 = 1375 dollars earned in total<BR>\n" );
document.write( "This confirms the second equation.\r<BR>\n" );
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document.write( "Since both equations have been satisfied, this confirms our answers.\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "25 advance tickets sold<BR>\n" );
document.write( "15 same-day tickets sold\r<BR>\n" );
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