M and M? No, it's M and N!!!

Algebra Level 3

During a contest, Brenda and her 2 older brothers, Benedict and Bob, were asked to each write down a number. Amazingly, the three numbers form an arithmetic sequence that decreases in the same order as their age (i.e. Benedict's number is the largest of the three, Bob's is in between while Brenda's is the smallest).

Interestingly, Benedict's number can be expressed as \(m+n\) and the sum of Benedict and Bob's numbers is \(m-n\). Moreover, Brenda's number can be expressed as \(mn\) while the sum of Bob and Brenda's, \(\frac{m}{n} \). If Bob's number can be expressed as -\(\frac{p}{q} \). where p and q are coprime positive integers, then what is p+q?

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