Question

A store has clearance items that have been marked down by 40%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?

Answer 1

`P_2 = (1-0.45) *0.6 P_o =0.55*0.60 P_o=0.33 P_o`

So the discount is 33% and we are paying 67% of the value. The reason is given by the relative change:

`\% Change = (|0.33P_o -P_o|)/(P_o)*100 =67\%`

Explanation:

First we have a first discount of 40% so then using this condition and assuming that
`P_o` represent the initial price, the price after the first discount
`P_1` is given by:

`P_1 = (1-0.4) P_o =0.6P_o`

That means 60% of the original value.

Now we have another discount of 45% for the 60% reamining after a 2 discount so let's
`P_2` represent the price after the second disccount we can can express this price in terms of
`P_1` or
`P_o` liek this:

`P_2 = (1-0.45) P_1=0.55 P_1`

`P_2 = (1-0.45) *0.6 P_o =0.55*0.60 P_o=0.33 P_o`

So the discount is 33% and we are paying 67% of the value. The reason is given by the relative change:

`\% Change = (|0.33P_o -P_o|)/(P_o)*100 =67\%`