Question 1209287: Hi
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.
Found 4 solutions by greenestamps, josgarithmetic, math_tutor2020, ikleyn:
Answer by greenestamps(13334)   (Show Source):
You can put this solution on YOUR website!
I don't know whether to laugh or cry when I see a math problem written with such terrible English that its meaning is a mystery.
"The number of students with cavities is 6 more than the number without cavities."
Okay, I get that.
x = # without cavities
x+6 = # with cavities
"When 1/8 of the number with cavities was treated they totaled the same number as the students without cavities."
I have absolutely no idea what that is supposed to say. My best guess as to what that terrible English is supposed to say is that 1/8 of the number with cavities is equal to the number without cavities; but that leads to nonsensical answers.
And the statement suggests that if a student with cavities is treated he no longer has cavities. That is not so. Once you have cavities, you have cavities. They don't disappear when they are "treated".
Now on to the question that is asked.
"How many of the original group of students have cavities and do not have cavities."
What is the word "original" doing there? The group of students never changes....
And finally, ignoring the "original", we have the question
"How many of the ... students have cavities and do not have cavities."
That is an absurd question. With the language used there, it is asking for the number of students who both have cavities and do not have cavities. You either have cavities or you don't; it can't be both.
ANSWER (without having to try to interpret the given information...): 0
Answer by josgarithmetic(39800)  (Show Source):
Answer by math_tutor2020(3835) (Show Source):
You can put this solution on YOUR website!
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 they totaled the same number as the students without cavities".
If we replace the word they with the phrase the remaining number with cavities, 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
Answer by ikleyn(53765)  (Show Source):
You can put this solution on YOUR website! .
Hi
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.
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This post is an example on how a Math problem SHOULD  be worded.
Lowest possible score to the problem's creator for his composition.
Normally, Math problem, formulated in a right way, should not create
questions about the meaning of the used terms.
Otherwise, the problem's creator is disqualified, without discussions.
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