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At a certain university, the ratio of the number of teaching [#permalink]

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04 Jun 2009, 21:11

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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]

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05 Jun 2009, 01:46

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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]

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16 Dec 2010, 14:36

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?

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: At a certain university, the ratio of the number of teaching [#permalink]

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26 Jan 2016, 10:18

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

Sorry, I couldn't delete this post!

same for me Please help. The phrase "must always be greater than" states it has to be 134 & not 133 what is the catch here?

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

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26 Jan 2016, 14:53

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The question states that the ratio must always be greater than 3:80, not the number of students (or burgers). So when you calculate the ratio \(\frac{5}{x}>\frac{3}{80}\), increasing the value of \(x\) will decrease the ratio \(\frac{5}{x}\), and decreasing the value of \(x\) will increase the ratio \(\frac{5}{x}\).

If you calculate the number of burgers to be 133.3, then decide whether to round up or down, understand what will happen to the ratio of \(\frac{5}{x}\).

If \(\frac{5}{133.33}=\frac{3}{80}\), and that is the minimum (because \(\frac{5}{x}\) must always be greater than \(\frac{3}{80}\)), what happens if you round \(x\) up to 134? Is \(\frac{5}{134}\) > or < \(\frac{3}{80}\)?

As explained above, if you increase \(x\) to 134, then the ratio \(\frac{5}{x}\) is decreased, and it will be less than the minimum of \(\frac{3}{80}\). If you round \(x\) down to 133, then the ratio \(\frac{5}{x}\) will increase, and you will not violate the condition that it must always be greater than \(\frac{3}{80}\).

Looking at it another way, if we know that the ratio of assistants to students must always be greater than 3:80, then we know that for any given number of assistants, there is a maximum number of students allowed. For every assistant, a maximum of 26.66 students are allowed (80/3). So if there is 1 assistant and 27 students, that is too many. 26 is the maximum number of students allowed if there is only 1 assistant in order to keep the ratio greater than 3:80. Using the same logic, if there are 5 assistants, then the maximum number of students allowed is 133.33. If there were 134 students that would be more than the maximum, therefore the maximum number of students allowed is 133.

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

\(\frac{Assistant}{Student} > \frac{3}{80}\)

\(\frac{5}{Student} > \frac{3}{80}\)

\(Student < \frac{(5*80)}{3}\)

\(Student < \frac{(400)}{3}\)

i.e. \(Student < 133.33\)

i.e. Maximum value of No. of students = 133

Answer: option D
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At a certain university, the ratio of the number of teaching [#permalink]

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25 Feb 2016, 12:56

Brute Force Method:

\(\frac{3}{80}\) As we are looking to a similar ratio for 5 assistants instead of 3, convert the both numerator (3) and denominator (80) to multiple of 5 by multiplying with 5

\(\frac{3*5}{80*5}\)equivalent to

\(\frac{15}{400}\)

Now as we need ratio for 05 assistants; again divide both numerator and denominator with 3. Pay attention to denominator which we need to answer:

\(\frac{5}{133.33}\) (Post division of both numerator and denominator with 03)

DONE

Maximum students could be 133 because if students 134 ratio would be less.

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

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