document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209287>Question 1209287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "The number of students with cavities is 6 more than the number without cavities. When 1/8 of the number with cavities was treated they totaled the same number as the students without cavities. How many of the original group of students have cavities and do not have cavities.  </SPAN>\n" );
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document.write( "As the other tutors point out, the wording seems a bit strange and leads to a non-integer result.\r<BR>\n" );
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document.write( "I think the issue with this problem is the sentence: \"When 1/8 of the number with cavities was treated <font color=red>they</font> totaled the same number as the students without cavities\".\r<BR>\n" );
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document.write( "If we replace the word <font color=red>they</font> with the phrase <font color=red>the remaining number with cavities</font>, then,<BR>\n" );
document.write( "c = starting number who have cavities<BR>\n" );
document.write( "n = starting number with no cavities<BR>\n" );
document.write( "(1/8)c = those who get dental treatment<BR>\n" );
document.write( "(7/8)c = those who don't get dental treatment<BR>\n" );
document.write( "(7/8)c = n \r<BR>\n" );
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document.write( "The \"The number of students with cavities is 6 more than the number without cavities\" is much more clear. It means that,<BR>\n" );
document.write( "c = n+6<BR>\n" );
document.write( "c = (7/8)c+6<BR>\n" );
document.write( "8c = 8*( (7/8)c+6 )<BR>\n" );
document.write( "8c = 7c + 48<BR>\n" );
document.write( "8c-7c = 48<BR>\n" );
document.write( "c = 48 students start off with cavities<BR>\n" );
document.write( "n = (7/8)*c = (7/8)*48 = 42 students in the original group do not have cavities<BR>\n" );
document.write( "This group of 42 doesn't include those who get dental treatment.\r<BR>\n" );
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document.write( "1/8 of those who do have cavities (48) get dental treatment, so (1/8)*48 = 6 lucky students get treatment <BR>\n" );
document.write( "48-6 = 42 unlucky students do not get treatment which equals the students who didn't have cavities at all.\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "48 start with cavities (6 get treatment)<BR>\n" );
document.write( "42 never had cavities at all<BR>\n" );
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