translate the given information into a system of equations. the question is below

Question

a college has a total of 320 employees, consisting of staff,administrators,and faculty members. the number of faculty members is the same as the number of staff and administrators combined, and the number of staff exceeds the number of administrators by 60. how many faculty members are there?

Answer 1

Let s = staff; let a = administrators; let f = faculty

 

Three unknowns means three equations.

#1) f + s + a = 320

#2) f = s + a

#3) s - 60 = a

 

From # 1, f = 320 - s - a

From # 2, f = s + a, so, 320 - s - a = s + a

Simplify: 320 = 2s + 2a

              160 = s + a

Therefore, from #1, f = 160

Therefore, s + a must = 160

From #3, s - 60 = a, so s + s - 60 = 160

Solve: 2s = 220, so, s = 110

Therefore, a = 50 (from #1)