Answer: The required discount is $819 and the rate of discount is 20.48%.
Step-by-step explanation: Given that a home theater system is marked down from $3999 to $3180.
We are to find the discount and the rate of discount.
The discount will be given by actual price minus the marked price.
We have
Actual price = $ 3999 and marked price = $3180.
So, the discount is given by
![\textup{Discount}=\$(3999-3180)=\$819](https://img.qammunity.org/2020/formulas/mathematics/college/i9bvc24gu2f6ouydw3k8jhr05wt3vvm7tt.png)
And the rate of discount is
![\textup{Rate of discount}=(819)/(3999)*100\%=20.48\%](https://img.qammunity.org/2020/formulas/mathematics/college/umaldv742crrqqruv854ttwy55sd0e6eja.png)
Thus, the required discount is $819 and the rate of discount is 20.48%.