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Ian went shopping for a new pair of sneakers. Sales tax where he lives is 
4%. If the price of the pair of sneakers is 
p dollars and cents, which expression does NOT represent the total price plus tax?

1+0.04 p

1.04 p

(1+0.04)p

p+0.04 p

Ian went shopping for a new pair of sneakers. Sales tax where he lives is 4% 4 \% . If the price of the pair of sneakers is p p dollars and cents, which expression does NOT represent the total price plus tax?\newline1+0.04p 1+0.04 p \newline1.04p 1.04 p \newline(1+0.04)p (1+0.04) p \newlinep+0.04p p+0.04 p

Full solution

Q. Ian went shopping for a new pair of sneakers. Sales tax where he lives is 4% 4 \% . If the price of the pair of sneakers is p p dollars and cents, which expression does NOT represent the total price plus tax?\newline1+0.04p 1+0.04 p \newline1.04p 1.04 p \newline(1+0.04)p (1+0.04) p \newlinep+0.04p p+0.04 p
  1. Understand Problem: First, let's understand the "Which expression does NOT represent the total price plus tax for a pair of sneakers priced at pp dollars and cents with a sales tax of 4%4\%?"
  2. Calculate Total Price: To calculate the total price including tax, we need to add the sales tax to the original price. The sales tax is 4%4\% of the original price, which is represented by 0.04p0.04p. Therefore, the correct expression to represent the total price including tax would be the original price pp plus the tax 0.04p0.04p, which is p+0.04pp + 0.04p.
  3. Simplify Expression: Now let's simplify the expression p+0.04pp + 0.04p. This is equivalent to 1p+0.04p1p + 0.04p, which can be combined as (1+0.04)p(1 + 0.04)p or 1.04p1.04p. Both expressions correctly represent the total price including tax.
  4. Evaluate Given Options: Let's evaluate each of the given options to see which one does NOT represent the total price plus tax:\newline11. 1+0.04p1+0.04p - This expression adds 11 to 0.040.04 times the price, which does not make sense in the context of calculating the total price including tax.\newline22. 1.04p1.04p - This expression correctly represents the total price including tax.\newline33. (1+0.04)p(1+0.04)p - This expression correctly represents the total price including tax.\newline44. p+0.04pp+0.04p - This expression correctly represents the total price including tax.
  5. Identify Incorrect Expression: From the evaluation, we can see that the first expression, 1+0.04p1+0.04p, does not correctly represent the total price plus tax. It incorrectly adds 11 to 0.040.04 times the price, pp, which is not a valid calculation for sales tax.

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