document.write( "Question 1025763: A petroleum company has two different sources of crude oil. The first source provides crude oil that is 65% hydrocarbons, and the second one provides crude oil that is 90% hydrocarbons. In order to obtain 170 gallons of crude oil that is 75% hydrocarbons, how many gallons of crude oil must be used from each of the two sources? \n" ); document.write( "
Algebra.Com's Answer #641085 by ikleyn(52790)\"\" \"About 
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\n" ); document.write( "A petroleum company has two different sources of crude oil. The first source provides crude oil that is 65% hydrocarbons, and the second one provides crude oil that is 90% hydrocarbons. In order to obtain 170 gallons of crude oil that is 75% hydrocarbons, how many gallons of crude oil must be used from each of the two sources?
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document.write( "Let x = volume of the crude oil that is 65% hydrocarbons (in gallons),\r\n" );
document.write( "and y = volume of the crude oil that is 90% hydrocarbons.\r\n" );
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document.write( "Then you have two equations:\r\n" );
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document.write( "    x +    y = 170,        (1)     (for the total volume)\r\n" );
document.write( "0.65x + 0.9y = 0.75*170.   (2)     (for the hydrocarbon content).\r\n" );
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document.write( "Rewrite simplifying (2):\r\n" );
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document.write( "    x +    y = 170,        (1')\r\n" );
document.write( "0.65x + 0.9y = 127.5.      (2')  \r\n" );
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document.write( "From (1'), express x = 170-y and substitute it into (2'). You will get a single equation for y:\r\n" );
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document.write( "0.65*(170-y) + 0.9y = 127.5\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "110.5 - 0.65y + 0.9y = 127.5,\r\n" );
document.write( "0.25y = 127.5 - 110.5,\r\n" );
document.write( "0.25y = 17,\r\n" );
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document.write( "y = \"17%2F0.25\" = 68 gallons.  It is the volume of the crude oil that is 90% hydrocarbons.\r\n" );
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document.write( "Now, the volume the crude oil that is 65% hydrocarbons is 170 - 68 = 102 gallons.\r\n" );
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