Let's break this problem down step by step.
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Initial Amount: Kat starts with $256.
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Refund from Dress: Kat returns a dress and receives a refund of $128.
\[ 256 + 128 = 384 \] So now, Kat has $384.
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Cost of Jacket: Kat buys a jacket for $98.
\[ 384 - 98 = 286 \] After buying the jacket, she has $286 left.
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Cost of Shoes: Kat then buys a pair of shoes for $105.
\[ 286 - 105 = 181 \] After buying the shoes, she has $181 left.
Therefore, the amount of money Kat has left to spend after buying the jacket and shoes is $181.00.