document.write( "Question 1126660: The state fair is a popular field trip destination. This year the senior classes at Berkner High School and Richardson High School both planned trips to the fair. Berkner filled 10 vans and 7 buses with 341 students, and Richardson filled 5 vans and 8 buses with 319 students. Each van and each bus carried the same number of students. Find the number of students in each van and bus. \n" ); document.write( "

Algebra.Com's Answer #742981 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "From the condition, you get these two equations\r\n" );
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document.write( "10*V + 7*B = 341    students     (1)    (V = is the van capacity;  B = the bus capacity)\r\n" );
document.write( " 5V  + 8*B = 319    students     (2)\r\n" );
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document.write( "Multiply eq(2) by 2  (both sides).  Keep eq(1) as is. You will get an EQUIVALENT system\r\n" );
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document.write( "10*V +  7*B = 341                (1')  \r\n" );
document.write( "10V  + 16*B = 638                (2')\r\n" );
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document.write( "Now subtract eq(1') from eq(2').  The terms  \"10V\" will cancel each other, and you will get a single equation for one unknown  B:\r\n" );
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document.write( "16B - 7B = 638 - 341\r\n" );
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document.write( "9B       = 297           =============>  B = 297/9 = 33.\r\n" );
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document.write( "Now from eq(1),  V =  = 11.\r\n" );
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document.write( "Answer.  The bus capacity is 33 students.  The van capacity is 11 students.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In the solution, I used the Elimination method to solve the system.\r
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\n" ); document.write( "\n" ); document.write( "So, on the way, you learned on how the Elimination method works.\r
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