First we must calculate how much Kelly will pay for the original purchase of $96.60. With 15% off, she will only need to pay $82.11.

Next we must figure out how much gum Kelly will buy to make $96.60 go over $100, and it turns out that 5 packs of gum will be the fewest to make her qualify for the 20% discount.

Buying 5 packs brings Kelly's total up to $100.55 and with a 20% discount she will end up paying $80.44 instead.

Subtract the higher amount ($82.11) by the lower amount ($80.44) aka [$82.11 - $80.44] and we are left with a difference of $1.67

By buying the 5 packs of gum Kelly will save $1.67

Answer: $1.67