because p,q,r is a prime number,pq+r=73 , ''the odd number'' multiply ''the odd number'' equal ''the odd number'' and ''the odd number'' plus ''the even number'' equal ''the odd number''. number.

We have 2 case:

case 1:r is even. so r = 2

pq+2=7

pq=71=1*71(eliminate)

case 2:p or q is even

example:p is even.so p=2

first:r=3

2*q+3=73

2*q=70

q=35

q isn't the prime number(eliminate)

second:r=5

2*q+5=73

2*q=68

q=34(eliminate)

third:r=7

2*q+7=73

2*q=66

q=33

fourth:r=9

2*q+9=73

2*q=64

q=32(eliminate)

fifth:r=11

2*q+11=73

2*q=62

q=31(possible)

so p+q+r=2+31+11=44