A retail item is offered at a discount of p percent (where p

Let x be the price of the item.
Final price after discount and sales tax = x * (1 - p/100) * 1.05

Let q be the percent discount which would result in the same final price.
Then,
x * (1 - p/100) * 1.05 = x * (1 - q/100)
=> 1.05 - 1.05p/100 = 1 - q/100
=> q/100 = 1.05p/100 - .05
=> q = 1.05p - 5

Hence , option C is correct.
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Appreciate your KUDOS.

Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.
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So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

Answer is C

Hi,

Please help me with understanding the question?
.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Please help me.

Thanks in Advance,
Rrsnathan.

Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?
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