Problem Solving

BTGmoderatorDC wrote: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
Source: GMAT Prep

$$t\,\,({\rm{ta}})\,\,,\,\,s\,\,\left( {{\rm{student}}} \right)\,\,\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\,\,\left( * \right)$$
$${t \over s} > {3 \over {80}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,{s_{\,\max }}\,\,\,{\rm{when}}\left( {{\rm{for}}} \right)\,\,\,t = 5$$

$$\frac{5}{s} > \frac{3}{{80}}\,\,\,\,\mathop \Leftrightarrow \limits^{80\,s\,\, > \,\,0} \,\,\,80 \cdot 5 > 3s\,\,\,\,\, \Leftrightarrow \,\,\,\,\,s < 5\left( {\frac{{78 + 2}}{3}} \right) = \underleftrightarrow {5\left( {26 + \frac{2}{3}} \right) = \,130 + \frac{{10}}{3}} = 133\frac{1}{3}\,$$
$$s < 133{1 \over 3}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = 133\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.