For this question, one can go for a Vienn Diagram to better visualize the problem.

So, the total number of students = 290

Students playing in a Band = Students just in the band + Students in both band and Orchestra.

The same applies to the Students in Orchestra. Hence Total number of students - Students in a Band = Students in just Orchestra.

=> Students just in orchestra = 80

Now Total students in Orchestra = 80 + x, where x is the number of students in both.

f(x) = 80+x represents the students in the Orchestra. The values in the table:

**Quote:**

The orchestra ---- The band and the orchestra

------------------------------------------------------------ 110

------------------------------------------------------------ 150

------------------------------------------------------------ 170

------------------------------------------------------------ 210

------------------------------------------------------------ 230

The values 230 and 150 satisfy the above equation. Hence, the total number in bands = 210, total number in Orchestra = 230 and the intersection of them both is 150. Please correct me if I am wrong

Regards,

Arpan

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