If an item is discounted by x% then:
The original price (OP) of the item is 100%.
Discounted by x% means 100% - x%, so the new price NP is OP*(100-x)%
NP = OP * (100-x)%
.
There are two versions of "discounted an additional 30%."
.
Version 1: The additional 30% discount hits the original price, not the x% off price. This means the sale price becomes (x + 30)% off, so the new price NP is OP(100-x-30)% or just OP(70-x)%
36.75 = 70(70-x)%
Don't forget that % means /100
36.75 = 70(70 - x)/100
36.75 = 0.7(70 - x)
36.75 / 0.7 = 70 - x
52.5 = 70 - x
52.5 + x = 70
x = 70 - 52.5
x = 17.5
Answer: The first discount x was 17.5%
.
Version 2: The additional 30% discount hits the x% off price, not the original price. This means the new price NP becomes OP*(100-x)%*(100-30)%. You have to hit the old price once for the x% discount, then hit it again for the 30% discount.
NP = OP * (100 - x)/100 * (100 - 30)/100
36.75 = 70 * (100 - x)/100 * 70/100
36.75 = (100 - x)/100 * 4900/100
36.75 = (100 - x)/100 * 49
36.75 = (100 - x) * 0.49
36.75 / 0.49 = 100 - x
75 = 100 - x
75 + x = 100
x = 100 - 75
x = 25
Answer: The first discount was 25%