document.write( "Question 1109449: Kiana and Jacobi each have a collection of identical red marbles and identical blue marbles. Kiana has a collection of 12 red marbles and 8 blue marbles weigh 70 grams. Jacobi collection of 20 red marble and 12 blue marbles weigh 110 grams. how much does each marble weigh? \n" ); document.write( "

Algebra.Com's Answer #724447 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "From the condition, you have this system of 2 equations\r\n" );
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document.write( "12*r +  8*b =  70     (1)\r\n" );
document.write( "20*r + 12*b = 110     (2)\r\n" );
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document.write( "Use the Elimination method.  For it, multiply eq(1) by 5 (both sides).  Multiply eq(2) by 3 (both sides).  You will get\r\n" );
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document.write( "60*r + 40*b = 350     (1')\r\n" );
document.write( "60*r + 36*b = 330     (2')\r\n" );
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document.write( "Now subtract eq(2') from eq(1')  (both sides).  The terms \"60*r\" will cancel each other.  (It is how the Elimination method works).\r\n" );
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document.write( "You will get a single equation for only one unknown\r\n" );
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document.write( "40b - 36b = 350 - 330\r\n" );
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document.write( "4b = 20    ====>  b =  = 5.\r\n" );
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document.write( "Then from eq(1)  \r\n" );
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document.write( "12r + 8*5 = 70  ====>  12r = 70-40 = 30  ====>  r =  = 2.5.\r\n" );
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document.write( "Answer.  Red marble weights 2.5 grams.   Blue marble weights 5 grams.\r\n" );
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document.write( "Check.   Checking is a necessary part of the solution.\r\n" );
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document.write( "         Make checking on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.   // On the way, you learned on how the Elimination method works.\r
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\n" ); document.write( "To see many other solved word problem reduced to systems of 2 equations in 2 unknowns, look into the lessons\r
\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( "    - 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( "    - Solving systems of non-linear equations by reducing to linear ones \r
\n" ); document.write( "\n" ); document.write( "    - System of equations helps to solve a problem for the Thanksgiving day\r
\n" ); document.write( "\n" ); document.write( "    - Using system of two equations to solve the problem for the day of April, 1 \r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns\r
\n" ); document.write( "\n" ); document.write( "in this site.\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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