Hypothesize why children went to work in these conditions during the industrial revolution.

Well, an obvious reason why children went to work during the Industrial revolution despite the conditions for work being horrible is the simple fact that families couldn't afford to survive in a lot of cases if it weren't for their children who would work as well. It was done out of necessity not out of pleasure. 

12 days because 1/4 is 25% of 100 if 100 is equal to 1 pound then multiply 3 by 4 which equals 12