document.write( "Question 1014146: mr.henson needs 400 grams of a 45% solution of alcohol by mixing 35% and 75% solutions. How much of each does he need? \n" ); document.write( "

Algebra.Com's Answer #630496 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Mr. Henson needs 400 grams of a 45% solution of alcohol by mixing 35% and 75% solutions. How much of each does he need?
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document.write( "Let x be the mass of 35% solution (in grams) and y be the mass of 75% solution (in grams) to be mixed.\r\n" );
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document.write( "Looking for the total mass you have this equation: x + y = 400. \r\n" );
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document.write( "Looking for the alcohol content you have the second equation: 0.35*x + 0.75*y = 0.45*400 = 180.\r\n" );
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document.write( "Combining both equations, you have this system of two equations in two unknowns\r\n" );
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document.write( "     x +      y = 400,   (1)\r\n" );
document.write( "0.35*x + 0.75*y = 180.   (2).\r\n" );
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document.write( "To solve it, multiply equation (1) by 0.35 (all the terms in both sides) and then distract from the equation (2).\r\n" );
document.write( "In this way you eliminate x and will obtain a single equation for y:\r\n" );
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document.write( "0.75*y - 0.35*y = 180 - 0.35*400,   or\r\n" );
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document.write( "0.4*y = 40.\r\n" );
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document.write( "Hence, y =  = 100.\r\n" );
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document.write( "Answer. 100 grams of 75% and 400-100 = 300 grams of 35% solutions are needed.\r\n" );
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