The dress is originally 160$, but we take 30% off which is that same as .3 .
To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.
48 is 30% of 160 so to find the new price of the dress we need to subtract
160 - 48 = 112. The new price of the dress is 112$.
Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$. 10% is also .1, so we will multiply 112 by .1 which equals 11.20.
As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.
For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.
Claire will be paying 108.36$ for the prom dress.