document.write( "Question 1132796: . Adult tickets cost 5 dollars and child tickets cost 2 dollars. The box office recorded $190 in ticket sales. A total of 50 tickets were sold. How many of those tickets were child tickets?
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Algebra.Com's Answer #749932 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Your first equation is\r\n" );
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document.write( "    x + y = 50     (counting the tickets)\r\n" );
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document.write( "Your second equation is your \"money\" equation, or \"revenue\"\r\n" );
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document.write( "   5x + 2y = 190    (dollars)\r\n" );
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document.write( "So, you have the system of 2 equations in 2 unknowns\r\n" );
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document.write( "    x + y  = 50,     (1)    and\r\n" );
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document.write( "   5x + 2y = 190.    (2)\r\n" );
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document.write( "There are different methods to solve the system.\r\n" );
document.write( "Since you are a beginner, I will show you the simplest method, which is the Substitution method.\r\n" );
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document.write( "From equation (1), express  y = 50-x  and substitute it into the second equation, replacing y there.  You will get\r\n" );
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document.write( "   5x + 2*(50-x) = 190.\r\n" );
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document.write( "Simplify it step by step and solve for x.\r\n" );
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document.write( "    5x + 100 - 2x = 190.\r\n" );
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document.write( "    5x - 2x = 190 - 100\r\n" );
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document.write( "    3x = 90  ====>  x = 90/3 = 30.\r\n" );
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document.write( "We just found x, or the number of adults. It is 30.\r\n" );
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document.write( "Now substitute the found value of x= 30 into equation (1). \r\n" );
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document.write( "   30 + y = 50\r\n" );
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document.write( "    y = 50-30 = 20\r\n" );
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document.write( "So, the remained number of children is 20.\r\n" );
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document.write( "ANSWER.  30 adults and 20 children.\r\n" );
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document.write( "CHECK.   30*5 + 20*2 = 150 + 40 = 190  dollars is your REVENUE, exactly as the problem states.\r\n" );
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document.write( "         Hence, the found values are the correct solution !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical ticket problem.\r
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\n" ); document.write( "\n" ); document.write( "For ticket problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) problems on tickets\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "From these lessons, learn on how to solve such problems once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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