To find the final selling price of the vest, we will apply the two discounts step-by-step:
1. Original Price:
The original price of the vest is [tex]\(\$80\)[/tex].
2. First Discount:
The store is having a 20% off sale. We need to calculate the price after applying the first discount.
A 20% discount means that you are paying 80% of the original price. We can express this as:
[tex]\[
\text{Price after first discount} = \text{Original Price} \times (1 - \text{Discount Rate})
\][/tex]
Using a discount rate of 20%, we get:
[tex]\[
\text{Price after first discount} = 80 \times (1 - 0.20) = 80 \times 0.80 = 64
\][/tex]
So, the price after the first discount is [tex]\(\$64\)[/tex].
3. Second Discount:
You have an additional coupon for a 20% discount off the lowest sale price. Now, we need to calculate the price after applying this second discount.
Again, a 20% discount means you are paying 80% of the latest sale price:
[tex]\[
\text{Final price} = \text{Price after first discount} \times (1 - \text{Discount Rate})
\][/tex]
Using the price after the first discount of \[tex]$64 and a discount rate of 20%, we get:
\[
\text{Final price} = 64 \times (1 - 0.20) = 64 \times 0.80 = 51.2
\]
Therefore, the final selling price of the vest is \(\$[/tex]51.20\).
So, the answer to the question is:
[tex]\[
\boxed{51.20}
\][/tex]
