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

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24 Oct 2010, 16:57

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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? A. 130 B. 131 C. 132 D. 133 E. 134

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 \(s_{max}=133\).

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 \(s_{max}=133\).

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

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11 Jan 2017, 21:54

Thank you for replying Bunuel. See, I understand the algebraic representation of the statement. My problem is

teachers/students > 3/80 means that for every 80 students, there are 3 teachers. therefore, for every 1 teacher, the maximum number of student can be 26.7 rounded off to 26 (cant take 27 coz then the condition wont sustain).Now, if for 1 teacher the max is 26, therefore for 5 teachers the max should be 130, no? Where am I going wrong ??

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

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15 Mar 2017, 01:55

I got 133 as answer. But if you compare the ratios. \frac{3}{80}=0.0375 1)\frac{5}{130}=0.0384 2)Will be less than 2nd option 3)Will be less than 2nd option 4)Will be less than 2nd option 5)Will be less than 2nd option Since we were told that ratio should be greater than \frac{3}{80} and only option 1 satisfies that. Not sure where i am wrong. Can someone help me understand this?

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

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15 Mar 2017, 02:04

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

let teaching assistant be t and s be the students then t/s > 3/80 given t=5 5/s>3/80 (400)/3 > s 133.33>s so s =133 answer D

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

We are given that the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80, and we need to determine the maximum number of students possible in a course that has 5 teaching assistants. Let’s use the following formula, in which t = 5 = the number of teaching assistants and s = the number of students.

t/s> 3/80

5/s > 3/80

400 > 3s

400/3 > s

133.33 > s

Since s must be a whole number, the largest possible value of s is 133.

Answer: D
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