document.write( "Question 1102672: Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244. What is the cost of a bunch of roses? What is the cost of a bunch of violets? How much would it cost Mac to purchase 2 bunches of roses and 3 violets? \n" ); document.write( "

Algebra.Com's Answer #717433 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Kaiden has sold 10 bunches of roses and 12 violets for a total of $380. Grayson has sold 6 bunches of roses and 8 violets for $244.
\n" ); document.write( "What is the cost of a bunch of roses? What is the cost of a bunch of violets? How much would it cost Mac to purchase
\n" ); document.write( "2 bunches of roses and 3 violets?
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document.write( "The condition gives you this system of 2 equations in 2 unknowns \r\n" );
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document.write( "10x + 12y = 380     (1)\r\n" );
document.write( " 6x +  8y = 244     (2)\r\n" );
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document.write( "I will solve it by the Elimination method. For it, multiply eq(1) by 3 (both sides). Multiply eq(2) by 5. You will get\r\n" );
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document.write( "30x + 36y = 1140    (3)\r\n" );
document.write( "30x + 40y = 1220    (4)\r\n" );
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document.write( "Next subtract eq(3) from eq(4).  The terms \"30x\" will cancel each other, and you will get a single equation for \"y\":\r\n" );
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document.write( "4y = 1220 - 1140 = 80  ====>  y =  = 20.\r\n" );
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document.write( "Then from eq(1)  10x = 380 - 12*20 = 140  ====>  x =  = 14.\r\n" );
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document.write( "Answer.  Bunch of roses costs $14.  Each violet costs $20.\r\n" );
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document.write( "         2 bunches of roses and 3 violets cost 2*$14 + 3*$20 = $88.\r\n" );
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