document.write( "Question 1163106: From a group of 440 students who took the exam, 300 passed English, 280 passed Spanish, 220 passed Math, 180 passed English and Spanish, 160 Spanish and Mathematics, 150 English and Mathematics and 100 passed English, Spanish and Mathematics. How many altogether passed at least one of these three subjects? \n" ); document.write( "
Algebra.Com's Answer #787085 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "In Venn diagram problems, the clues are nearly always given in the reverse\r\n" );
document.write( "order from the order that you need them, so we begin by rearranging them in\r\n" );
document.write( "reverse order: \r\n" );
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document.write( "100 passed English, Spanish and Mathematics, that's e\r\n" );
document.write( "   So we put 100 for e\r\n" );
document.write( "150 English and Mathematics, that's d+e\r\n" );
document.write( "   So we put 150-100=50 for d\r\n" );
document.write( "160 Spanish and Mathematics, that's, e+f\r\n" );
document.write( "   So we put 160-100=60 for f \r\n" );
document.write( "180 passed English and Spanish, that's b+e\r\n" );
document.write( "   So we put 180-100=80 for b \r\n" );
document.write( "220 passed Math, that's d+e+f+g\r\n" );
document.write( "   So we put 220-50-100-60=10 for g \r\n" );
document.write( "280 passed Spanish, that's b+c+e+f \r\n" );
document.write( "   So we put 280-80-100-60=40 for c\r\n" );
document.write( "300 passed English, that's a+b+d+e\r\n" );
document.write( "   So we put 300-80-100-50=70 for a\r\n" );
document.write( "440 students took the exam, that's a+b+c+d+e+f+g+h\r\n" );
document.write( "   So we put 440-70-80-40-50-100-60-10=30 for h\r\n" );
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document.write( "The question is:\r\n" );
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document.write( "How many altogether passed at least one of these three subjects?\r\n" );
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document.write( "That's all but the h=30 who didn't pass any. That's 440-30=410\r\n" );
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document.write( "Edwin
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