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At a certain university, the ratio of the number of teaching [#permalink]
04 Jun 2009, 20:11

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Difficulty:

55% (hard)

Question Stats:

65% (01:51) correct
35% (00:54) wrong based on 154 sessions

At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university , what is the maximum number of students possible in a course that has 5 teaching assistants?

Re: problem solving question on ratios [#permalink]
05 Jun 2009, 00:46

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Not sure whether this is the best possible way but just the way how I solve it.

Teaching Assistants = TA Students = S

Let assume the ratio of TA/S = 3/80 (Just putting aside the requirement it must be greater)

Let say x be the maximum no of students possible with 5 teaching assistants = 3/80 = 5/x

x = 400/3 = 133.33. Now for ratio to be greater than 3/80 reduce the denominator. So just rounded it to lowest integer as number of student can't be in decimal. The new ratio is 5/133, which is less than 3/80 thus, 133 is the maximum number of students possible.

Re: problem solving question on ratios [#permalink]
16 Dec 2010, 13:36

can someone explain in further detail the relationship between the teaching assistants to the number of students in any course must always be greater than 3:80 and how to reason through this portion? I understand how to solve for x. Once I was at this point I think was stumped on which number to select and inevitably chose to round up. My rational being .33 of a student is not possible therefore it must represent the position of an entire student. Thoughts? Help?

Re: problem solving question on ratios [#permalink]
16 Dec 2010, 13:47

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Expert's post

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spyguy wrote:

can someone explain in further detail the relationship between the teaching assistants to the number of students in any course must always be greater than 3:80 and how to reason through this portion? I understand how to solve for x. Once I was at this point I think was stumped on which number to select and inevitably chose to round up. My rational being .33 of a student is not possible therefore it must represent the position of an entire student. Thoughts? Help?

At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants? A. 130 B. 131 C. 132 D. 133 E. 134

Given: \frac{assistants}{students}>\frac{3}{80} --> assistants=5, so \frac{5}{s}>\frac{3}{80} --> s_{max}=?

\frac{5}{s}>\frac{3}{80} --> s<\frac{5*80}{3}\approx{133.3} --> so s_{max}=133.

Answer: D.

\frac{assistants}{students}>\frac{3}{80} relationship means that if for example # of assistants is 3 then in order \frac{assistants}{students}>\frac{3}{80} to be true then # of students must be less than 80 (so there must be less than 80 students per 3 assistants) on the other hand if # of students is for example 80 then the # of assistants must be more than 3 (so there must be more than 3 assistants per 80 students).

At a certain restaurant, the ratio of the number of chefs to the number of burgers on any day must always be greater than 3:80. At this restaurant, what is the maximum number of burgers possible on a day that has 5 chefs.

A) 130 B) 131 C) 132 D) 133 E) 134

Please help. The phrase "must always be greater than" is completely throwing me off.

[EDIT] The same problem has been solved elsewhere: problem-solving-question-on-ratios-79240.html

Sorry, I couldn't delete this post! _________________

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Re: Chefs to burgers [#permalink]
12 Mar 2012, 22:49

boomtangboy wrote:

hi,

Give me a Big Kudoos Meal Combo if this helps

Hi BoomTang, great answer! +1 _________________

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"There is no alternative to hard work. If you don't do it now, you'll probably have to do it later. If you didn't need it now, you probably did it earlier. But there is no escaping it."

Re: Chefs to burgers [#permalink]
12 Mar 2012, 23:40

Expert's post

budablasta wrote:

At a certain restaurant, the ratio of the number of chefs to the number of burgers on any day must always be greater than 3:80. At this restaurant, what is the maximum number of burgers possible on a day that has 5 chefs.

A) 130 B) 131 C) 132 D) 133 E) 134

Please help. The phrase "must always be greater than" is completely throwing me off.

[EDIT] The same problem has been solved elsewhere: problem-solving-question-on-ratios-79240.html

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