Step 1 :Calculate the final price of the article at the electronic store after applying all the discounts: \(978 \times (1 - 0.066) \times (1 - 0.113) \times (1 - 0.055) = 765.66916818\)
Step 2 :Calculate the final price of the article at the competitor's store after applying their discounts: \(950 \times (1 - 0.101) \times (1 - 0.054) = 807.9313\)
Step 3 :Find the difference between the two final prices to determine the additional discount needed for the competitor to price match: \(807.9313 - 765.66916818 = 42.26213182\)
Step 4 :\(\boxed{42.26}\) is the additional amount of discount needed for the competitor to price match (option c)