document.write( "Question 1127524: Adrian, Nathan, and Brian bought lunch from the concession stand. Adrian paid $5.50 for burgers, fries and a drink; Nathan paid $4.00 for a burger and a drink; and Brian paid $4.25 for a burger and fries.
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\n" ); document.write( "b)solve the system of equations to determine the cost of each food item.
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Algebra.Com's Answer #743947 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " I will show you MUCH FASTER way to solve the system !\r
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document.write( "The setup is still the same:\r\n" );
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document.write( "Let burgers be x, fries y, and drink z\r\n" );
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document.write( "x + y + z = 5.50       (1)\r\n" );
document.write( "x + 0 + z = 4.00       (2)\r\n" );
document.write( "x + y + 0 = 4.25       (3)\r\n" );
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document.write( "a)  To find \"y\", subtract eq(2) from eq(1). You will get\r\n" );
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document.write( "    y = 5.50 - 4.00 = 1.50.     The unknown \"y\" is just found !\r\n" );
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document.write( "b)  To find \"z\", subtract eq(3) from eq(1). You will get\r\n" );
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document.write( "    z = 5.50 - 4.25 = 1.25.     The unknown \"z\" is just found !\r\n" );
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document.write( "c)  To find \"x\", substitute the found values of y and z into eq(1) to get\r\n" );
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document.write( "    x + 1.50 + 1.25 = 5.50,   which implies\r\n" );
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document.write( "    x = 5.50 - 1.50 - 1.25 = 2.75.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Just solved (!)\r
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\n" ); document.write( "\n" ); document.write( "The structure of the system (1), (2), (3) is such that elimination works very straightforward for \"y\" and \"z\" (!).\r
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\n" ); document.write( "\n" ); document.write( "An educated student must see it after a quick look into the system.\r
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\n" ); document.write( "\n" ); document.write( "An experienced student must recognize this way of solving immediately after reading the condition even without writing the system.\r
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\n" ); document.write( "\n" ); document.write( "This problem is, actually, for MENTAL solution.\r
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