Wendy made some badges for an event. She sold $$\frac{5}{7}$$ of the badges on the first day and $$\frac13$$ of the remaining badges on the second day. She then made an additional $$354$$ badges and in the end, she had $3$ times the number of badges she made at first. How many badges did she make for the event at the beginning? 
Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base