Hi Aaron,
Bunuel's explanation is, of course, correct. The answer is D.
Think of it this way:
If you have a ratio \(\frac{a}{b}\), and you want to
increase the value of that ratio, there are two ways you can do that. You can either increase the numerator or
decrease the denominator. In our case, we want to choose the denominator so that the resulting ratio is
less than the given value \(\frac{3}{80}\). To do that we will have to increase the denominator as much as we can so that the ratio \(\frac{assistants}{students}\) is still greater than \(\frac{3}{80}\). But if we increase the denominator too much the ratio of assistants to students will drop below our limit of \(\frac{3}{80}\).
Imagine a simpler scenario where the target ratio wasn't \(\frac{3}{80}\), but instead \(\frac{5}{80}\). In that case the greatest number of students that would be allowed and still maintain the ratio of assistants to students
greater than \(\frac{5}{80}\) would be 79. One more student and the ratio would be equal to, not greater than \(\frac{5}{80}\).
In our problem, we want the
maximum number of students such that the ratio \(\frac{assistants}{students}>\frac{3}{80}\). You can solve this algebraically, as has been done above to find that students must be
less than 133.3. The largest integer less than 133.3 is 133. If we decrease the students down to 130, then the ratio will indeed be larger than the target of \(\frac{3}{80}\), but we still have space to add more students and still maintain the ratio greater than \(\frac{3}{80}\).
I hope it helps!
aaronTgmaT wrote:
Hello Bunuel,
As per your explanation here, then max should be A: 130 to be greater than 3/80. Is my thinking correct.
Bunuel wrote:
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).
Hope it's clear.