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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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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

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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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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

Re: At a certain university, the ratio of the number of teaching [#permalink]
05 Apr 2015, 05:25

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