In an examination, a student’s scores in Mathematics (M) and Physics (P) must satisfy the following conditions:
1. The average score should be at least 75.
2. The total score must not exceed 155.
3. The Physics score is known to lie in the interval 68≤P≤72.
Answer the following.
a. (i) Translate each condition into a mathematical inequality in M and/or P.
b. (ii) Using the inequalities from part (i) together with the given range for P, deduce the complete range of values that M can take.
c. (iii) Determine whether M can be an integer prime number. Give reasons for your answer based on the range found in part (ii).