something equalling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21
do you mean x+13=21 (mod 34) ?
clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100
so 3 solutions
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13n-1 = 9k
13n-9k = 1
Using the Euclidean algorithm
13(7) - 9(10) = 91-90 = 1
so 7 boxes and 9 bags