How many received medals in <strong>EXACTLY</strong> two of the three sports ?
Consider the following for the next three (03) items that follow : A university awarded medals in basket ball, football and volleyball. <strong>ONLY</strong> x students (x \lt 6) got medal in <strong>ALL</strong> the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x+15) medals in football and (x+25) medals in volleyball.
- A. 30-4x
- B. 35-7x
- C. 40-7x ✓
- D. 45-5x
Correct Answer: C. 40-7x
Explanation
Let T be total students (15x). We know T = n(B) + n(F) + n(V) - n(\text{exactly two}) - 2n(\text{all three}). Substituting the values: 15x = 5x + (4x+15) + (x+25) - n(\text{exactly two}) - 2(x). Simplifying gives 15x = 10x + 40 - n(\text{exactly two}) - 2x, so n(\text{exactly two}) = 40 - 7x.
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