Final answer:
To find the number of research assistants employed by the university, set up a system of equations. Let R be the number of research assistants and T be the number of teaching assistants. Use the equation T + R = 560 and the fact that T = 3R to solve for R.
Step-by-step explanation:
To find the number of research assistants employed by the university, we need to set up a system of equations. Let's assume that the number of research assistants is represented by the variable 'R'. Since there are three times as many teaching assistants as research assistants, the number of teaching assistants can be represented by the variable 'T', which is equal to 3R. Together, the total number of teaching assistants and research assistants is 560, so we can write the equation T + R = 560.
Substituting the value of T from the equation T = 3R, we get 3R + R = 560. Simplifying this equation, we get 4R = 560. Dividing both sides by 4, we find that R = 140. Therefore, the university employs 140 research assistants.