document.write( "Question 1144628: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. How much does each type of box weigh? \n" ); document.write( "
Algebra.Com's Answer #765797 by ikleyn(52814)\"\" \"About 
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document.write( "Without any explanations, it is clear that from the condition you have these 2 equations in 2 unknowns\r\n" );
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document.write( "    6x + 5y = 145   kilograms     (1)\r\n" );
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document.write( "    2x + 3y =  57   kilograms     (2)\r\n" );
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document.write( "To solve it, use Elimination method.\r\n" );
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document.write( "For it, multiply equation (2) by 3 (both sides).  Keep equation (1) as is\r\n" );
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document.write( "    6x + 5y = 145                 (1')\r\n" );
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document.write( "    6x + 9y = 171                 (2')\r\n" );
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document.write( "From equation (2') subract equation (1').  The terms  \" 6x \" will cancel each other, and\r\n" );
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document.write( "you will get one single equation for \"y\"\r\n" );
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document.write( "    9y - 5y = 171 - 145,   or\r\n" );
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document.write( "    4y       = 26\r\n" );
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document.write( "     y       = 26/4 = 6.5.\r\n" );
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document.write( "Thus small box weights 6.5 kilograms.\r\n" );
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document.write( "Now substitute it into equation (2) to find \"x\" :\r\n" );
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document.write( "    2x + 3*6.5 = 57,\r\n" );
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document.write( "    2x = 57 - 3*65 = 37.5.\r\n" );
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document.write( "     x             = 37.5/2 = 18.75.\r\n" );
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document.write( "ANSWER.  Large box weights  18.75 kilograms.  Small box weights  6.5 kilograms.\r\n" );
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document.write( "CHECK.  Equation (1) :  6*18.75 + 5*6.5 = 145 kilograms.   ! Correct !\r\n" );
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document.write( "        Equation (2) :  2*18.75 + 3*6.5 = 57 kilograms.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On the way, you learned on how the Elimination method works.\r
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\n" ); document.write( "On solving systems of linear equations in two unknowns see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of a linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of a linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solving word problems using linear systems of two equations in two unknowns \r
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\n" ); document.write( "\n" ); document.write( "    - Oranges and grapefruits \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( "    - Using systems of equations to solve problems on shares \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on investment\r
\n" ); document.write( "\n" ); document.write( "    - Two mechanics work on a car \r
\n" ); document.write( "\n" ); document.write( "    - The Robinson family and the Sanders family each used their sprinklers last summer\r
\n" ); document.write( "\n" ); document.write( "    - Roses and vilolets \r
\n" ); document.write( "\n" ); document.write( "    - Counting calories and grams of fat in combined food\r
\n" ); document.write( "\n" ); document.write( "    - A theater group made appearances in two cities\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns \r
\n" ); document.write( "\n" ); document.write( "    - One unusual problem to solve using system of two equations \r
\n" ); document.write( "\n" ); document.write( "    - Solving mentally word problems on two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "in this site. They all are free of charge.\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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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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