document.write( "Question 1149259: A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1600 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week? \n" ); document.write( "
Algebra.Com's Answer #770602 by ikleyn(52786)\"\" \"About 
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document.write( "Let x = the number of gallons consumed by the 1-st car and y = that for the 2-nd car.\r\n" );
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document.write( "Then you have this system of 2 equations in 2 unknowns\r\n" );
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document.write( "      x +   y =   65       (1)    (65 gallons of gas, total)\r\n" );
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document.write( "    40x + 15y = 1600       (2)    (miles, total)\r\n" );
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document.write( "There are many methods to solve the system.\r\n" );
document.write( "For example, you may use the Elimination method.\r\n" );
document.write( "For it, multiply eq(1) by 40 (both sides).  Keep eq(2) as is\r\n" );
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document.write( "    40x + 40y = 65*40      (1')   \r\n" );
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document.write( "    40x + 15y = 1600       (2')    \r\n" );
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document.write( "Next, subtract eq(2') from eq(1).  You will get\r\n" );
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document.write( "          40y - 15y = 65*40 - 1600 \r\n" );
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document.write( "          25y        = 1000\r\n" );
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document.write( "            y        = 1000/25 = 40.\r\n" );
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document.write( "ANSWER.  2-nd car consumed 40 gallons of gas;  1-st car consumed  the rest  65-40 = 25 gallons.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To learn on how to algebreze and to solve similar problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the 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( "    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns\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
\n" ); document.write( "\n" ); document.write( "in this site.\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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