12 ...4)⇒ e + f = 15 ...5)⇒ d + e = 20 ...6)By USING (1) + (2) + (3) – (4) – (5) – (6)⇒ a + b + c + d + f + g = 60 + 50 + 48 – 12 – 15 - 20 = 111Total number of students in school = a + b + c + d + f + g + e = 111 + e.Maximum number of students will depend on the maximum value of e.From the EQUATIONS (4), (5) and (6) we have the following three cases:Case 1: Let b = 0⇒ e = 12.By substituting the value of e in (5), we get⇒ f = 15 – e = 3By substituting the value of e in (5), we get⇒ d = 20 – e = 8Case 2: Let f = 0⇒ e = 15.By substituting the value of e in (4), we get⇒ b = 12 – e = -3We got b as negative, so we need to discard this case ∵ b ≥ 0.Case 3: Let d = 0⇒ e = 20.By substituting the value of e in (4), we get⇒ b = 12 – e = -8We got b as negative, so we need to discard this case ∵ b ≥ 0.So the maximum possible value of e is from case 1 i.e. e = 12.∴ Maximum possible number of students in school = 111 + e = 123.