document.write( "Question 1109271: daniel and kayla each improved their yards by planting daylilies and shrubs. they bought their supplies from the same store. daniel spent $156 on 8 daylilies and 14 shrubs. kayla spent $162 on 14 daylilies and 6 shrubs. what is the cost of one daylily and the cost of one shrub?
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Algebra.Com's Answer #724261 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "From the condition, you have the system of 2 equations in 2 unknowns\r\n" );
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document.write( " 8*d + 14*s = 156,    (1)    (Daniel' spending)\r\n" );
document.write( "14*d +  6*s = 162.    (2)    (Kayla' spending)\r\n" );
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document.write( "To solve the system, multiply equation (1) by 7 (both sides).  multiply equation (2) by 4 (both sides).  The modified system is\r\n" );
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document.write( "56*d + 98*s = 1092,    (3)   \r\n" );
document.write( "56*d + 24*s =  648.    (4) \r\n" );
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document.write( "Now subtract eq(4) from eq(3) (both sides).  The terms \"56*d\" in both equations will cancel each other, and \r\n" );
document.write( "you will get a single equation for only one unknown \"s\" (it is how the Elimination method works):\r\n" );
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document.write( "74s = 1092 - 648  = 444  ====>  s =   = 6.\r\n" );
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document.write( "Thus you found that one shrub costs $6.\r\n" );
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document.write( "Then from eq(1),   8d = 156 - 14*6 = 72  and  d =  = 9.\r\n" );
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document.write( "Answer.  One daylily costs $9  and  one shrub costs $6.\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( "On solving systems of two linear equations in two unknowns and related word problems 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( "    - 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( "    - 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
\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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