Question 1209287
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As the other tutors point out, the wording seems a bit strange and leads to a non-integer result.


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".


If we replace the word <font color=red>they</font> with the phrase <font color=red>the remaining number with cavities</font>, then,
c = starting number who have cavities
n = starting number with no cavities
(1/8)c = those who get dental treatment
(7/8)c = those who don't get dental treatment
(7/8)c = n 



The "The number of students with cavities is 6 more than the number without cavities" is much more clear. It means that,
c = n+6
c = (7/8)c+6
8c = 8*( (7/8)c+6 )
8c = 7c + 48
8c-7c = 48
c = 48 students start off with cavities
n = (7/8)*c = (7/8)*48 = 42 students in the original group do not have cavities
This group of 42 doesn't include those who get dental treatment.


1/8 of those who do have cavities (48) get dental treatment, so (1/8)*48 = 6 lucky students get treatment 
48-6 = 42 unlucky students do not get treatment which equals the students who didn't have cavities at all.



Answer:
48 start with cavities (6 get treatment)
42 never had cavities at all
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