Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?a)0.88pb)p/0.88c)(0.8)(1.08)pd)Correct answer is option 'D'. Can you explain this answer?

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Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?

a)
0.88p
b)
p/0.88
c)
(0.8)(1.08)p
d)

Correct answer is option 'D'. Can you explain this answer?

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Alma bought a laptop computer at a store that gave a 20 percent discou...

Let x be the original price of the computer, in dollars. The discounted price is 20 percent off the original price, so x - O.Zx = 0.8x is the discounted price, in dollars. The sales tax is 8 percent of the discounted price, so 0.08(0.8x) represents the sales tax Alma paid. The price p, in dollars, that Alma paid the cashiers is the sum of the discounted price and the tax: p = 0.8x + (0.08)(0.8x) which can be rewritten as p = 1.08(0.8x). Therefore, the original price, x, of the computer, in dollars, can be written as

in terms of p.
Choices A, B, and C are incorrect. The expression in choice A represents 88% of the amount Alma paid to the cashier, and can be obtained by subtracting the discount of 20% from the original price and adding the sales tax of 8%. However, this is incorrect because 8% of the tax is over the discounted price, not the original one. The expression in choice B is the result of adding the factors associated with the discount and sales tax, 0.8 and .08, rather than multiplying them. The expression in choice C results from assigning p to represent the original price of the laptop, rather than to the amount Alma paid to the cashier.

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