There are 153 students in the graduating class this year at Statsville High School. Mr. Pascal chose to carry out a survey among the graduating students and found the following:

• 85 graduates had taken a Grade 12 Science Course
• 71 graduates had taken a Grade 12 French Course
• 54 graduates had taken a Grade 12 Mathematics Course
• 40 graduates had taken both a Grade 12 Science and French Course
• 32 graduates had taken both a Grade 12 Science and Mathematics Course
• 20 graduates had taken both a Grade 12 French and Mathematics Course
• 16 graduates had not taken any Grade 12 Mathematics, French, or Science courses

How many graduates took all three courses: Grade 12 Mathematics, French, and Science?

An algebraic solution is required to isolate the unknown variable x in this Venn diagram problem.

Make a correctly labeled Venn diagram with a title, a legend, and all the necessary "let x" instructions. Avoid using trial and error procedures and stick to algebraic methods to find the unknown variable, x. A solution based on algebra is required. Make a final statement/conclusion. (This is worth 15 marks and will be marked for precision and explanation.) Preferably, please use the Venn diagram formula below when needed:

Some Important Formulae: For any three sets A, B, C. (i) n(A U B) = n(A) + n(B) - n(An B) (ii) If An B = Q, then n(A U B) = n(A) + n(B) (iii) n(A - B) + n(An B) = n(A) (iv) n(B - A) + n(An B) = n(B) (v) n(A UB) = n(A - B) + n(An B) + n(B - A) (vi) n( A U B UC) = n(A) + n(B) + n(C) - n(An B) - n(Bn C)- n(C n A) + n(An B n C)