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Lauren went shopping for a new phone. Sales tax where she lives is 
6.5%. If the price of the phone is 
p dollars and cents, which expression does NOT represent the total price plus tax?

1+0.065 p

(1+0.065)p

1.065 p

p+0.065 p

Lauren went shopping for a new phone. Sales tax where she lives is 6.5% 6.5 \% . If the price of the phone is p p dollars and cents, which expression does NOT represent the total price plus tax?\newline1+0.065p 1+0.065 p \newline(1+0.065)p (1+0.065) p \newline1.065p 1.065 p \newlinep+0.065p p+0.065 p

Full solution

Q. Lauren went shopping for a new phone. Sales tax where she lives is 6.5% 6.5 \% . If the price of the phone is p p dollars and cents, which expression does NOT represent the total price plus tax?\newline1+0.065p 1+0.065 p \newline(1+0.065)p (1+0.065) p \newline1.065p 1.065 p \newlinep+0.065p p+0.065 p
  1. Calculate Total Price: Identify the correct way to calculate the total price including sales tax.\newlineTo find the total price including tax, you multiply the price by 11 plus the tax rate.\newlineCalculation: Total price = p×(1+tax rate)p \times (1 + \text{tax rate})\newlineTax rate given is 6.5%6.5\%, or 0.0650.065 in decimal form.
  2. Check First Expression: Check the first expression to see if it represents the total price plus tax.\newlineFirst expression: 1+0.065p1 + 0.065 p\newlineThis expression adds 11 dollar to 6.5%6.5\% of the price, which does not correctly calculate the total price including tax.
  3. Check Second Expression: Check the second expression to see if it represents the total price plus tax.\newlineSecond expression: (1+0.065)p(1 + 0.065)p\newlineThis expression multiplies the price by 11 plus the tax rate, which is the correct way to calculate the total price including tax.
  4. Check Third Expression: Check the third expression to see if it represents the total price plus tax.\newlineThird expression: 1.065p1.065 p\newlineThis expression multiplies the price by 1.0651.065, which is equivalent to multiplying the price by 11 plus the tax rate, and thus correctly calculates the total price including tax.
  5. Check Fourth Expression: Check the fourth expression to see if it represents the total price plus tax.\newlineFourth expression: p+0.065pp + 0.065 p\newlineThis expression adds 6.5%6.5\% of the price to the original price, which is the correct way to calculate the total price including tax.
  6. Identify Incorrect Expression: Identify the expression that does NOT represent the total price plus tax.\newlineThe first expression, 1+0.065p1 + 0.065 p, does not correctly calculate the total price including tax because it adds 11 dollar to 6.5%6.5\% of the price instead of multiplying the entire price by 11 plus the tax rate.

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