The prime numbers p, q, r satisfy the simultaneous equations
pq + pr = 80 and pq + qr = 425. find the value of p + q + r.

Pq + pr = 80  => p (q+r) = 80
pq + qr = 425 => q (p+r ) = 425

Factorize 80 with having one factor as prime number
80 =  2 * 40 = 5 *16 

Factrorize 425 with having one factor as prime number
425 = 5 * 85 = 17 * 25...

Therfore, p has to be 2.
q = 17 and r= 23...
p + q +r = 2 + 17+ 23 = 42