SOLUTION: A two-digit positive integer x has the property that when 109 is divided by x, the remainder is 4. What is the sum of all such two-digit positive integers x?

        QUOTIENT
DIVISOR)DIVIDEND
        ##
         ##       
         REMAINDER

DIVIDEND = QUOTIENT×DIVISOR + REMAINDER


           q
       x)109
         ##
          ##
           4

109 = q∙x + 4

105 = q∙x

105 = 3∙5∙7

The only possible two digit numbers we can make
from multiplying, using 3,5, and 7 are 

3∙5=15, 3∙7=21, and 5∙7=35

     7             5              3
15)109        21)109         35)109 
   105           105            105 
     4             4              4

Answer = 15+21+35 = 71

Edwin