Choose the best answer. If necessary, use the paper you were given.
Doreen bought a dress priced at $89 and a skirt priced at $36. She paid a total of $135 for the dress and the skirt, including sales tax. What was the sales tax rate?
- A. 6%
- B. 7%
- C. 8%
- D. 9%
Correct Answer & Rationale
Correct Answer: C
To determine the sales tax rate, first calculate the total cost of the dress and skirt without tax: $89 + $36 = $125. Doreen paid $135, which means the sales tax was $135 - $125 = $10. To find the sales tax rate, divide the tax amount by the pre-tax total: $10 / $125 = 0.08, or 8%. Option A (6%) is incorrect as it would result in a lower tax amount. Option B (7%) also yields a tax amount that is too low. Option D (9%) would produce a tax amount exceeding $10, making it incorrect. Thus, the only option that accurately reflects the calculated sales tax rate is 8%.
To determine the sales tax rate, first calculate the total cost of the dress and skirt without tax: $89 + $36 = $125. Doreen paid $135, which means the sales tax was $135 - $125 = $10. To find the sales tax rate, divide the tax amount by the pre-tax total: $10 / $125 = 0.08, or 8%. Option A (6%) is incorrect as it would result in a lower tax amount. Option B (7%) also yields a tax amount that is too low. Option D (9%) would produce a tax amount exceeding $10, making it incorrect. Thus, the only option that accurately reflects the calculated sales tax rate is 8%.
Other Related Questions
If a +√x= b then x =
- A. √b-√a
- B. √(b-1)
- C. (b-a)²
- D. b²-a²
Correct Answer & Rationale
Correct Answer: C
To solve for \( x \) in the equation \( a + \sqrt{x} = b \), we first isolate \( \sqrt{x} \) by rearranging the equation to \( \sqrt{x} = b - a \). Squaring both sides gives \( x = (b - a)^2 \), which corresponds to option C. Option A, \( \sqrt{b} - \sqrt{a} \), does not account for squaring the expression and thus cannot represent \( x \). Option B, \( \sqrt{(b-1)} \), is unrelated to the original equation and lacks the necessary operations. Option D, \( b^2 - a^2 \), applies the difference of squares incorrectly and does not solve for \( x \) directly.
To solve for \( x \) in the equation \( a + \sqrt{x} = b \), we first isolate \( \sqrt{x} \) by rearranging the equation to \( \sqrt{x} = b - a \). Squaring both sides gives \( x = (b - a)^2 \), which corresponds to option C. Option A, \( \sqrt{b} - \sqrt{a} \), does not account for squaring the expression and thus cannot represent \( x \). Option B, \( \sqrt{(b-1)} \), is unrelated to the original equation and lacks the necessary operations. Option D, \( b^2 - a^2 \), applies the difference of squares incorrectly and does not solve for \( x \) directly.
The average of 5 numbers is 11. Which of the following must be true?
- A. The range of the 5 numbers is 55.
- B. The sum of the 5 numbers is 55.
- C. The median of 5 numbers is 11.
- D. The mode of 5 numbers is 11.
Correct Answer & Rationale
Correct Answer: B
To find the average of 5 numbers, you sum them and divide by 5. If the average is 11, the total sum must be 5 times 11, which equals 55. Thus, option B is true. Option A is incorrect; the range is the difference between the highest and lowest numbers, which can vary regardless of the average. Option C is also not necessarily true; the median, or middle value, can differ from the average depending on the distribution of the numbers. Option D is incorrect; the mode, or most frequently occurring number, does not have to be the same as the average.
To find the average of 5 numbers, you sum them and divide by 5. If the average is 11, the total sum must be 5 times 11, which equals 55. Thus, option B is true. Option A is incorrect; the range is the difference between the highest and lowest numbers, which can vary regardless of the average. Option C is also not necessarily true; the median, or middle value, can differ from the average depending on the distribution of the numbers. Option D is incorrect; the mode, or most frequently occurring number, does not have to be the same as the average.
Which of the following is equivalent to 12x +8?
- A. 4(3x+2)
- B. 4(3x+8)
- C. 4(3x+2x)
- D. 20x
Correct Answer & Rationale
Correct Answer: A
To determine the equivalent expression for \(12x + 8\), we can factor out the greatest common factor, which is 4. Option A, \(4(3x + 2)\), simplifies to \(12x + 8\) when distributed, making it equivalent to the original expression. Option B, \(4(3x + 8)\), simplifies to \(12x + 32\), which is not equivalent. Option C, \(4(3x + 2x)\), simplifies to \(4(5x)\) or \(20x\), which is also not equivalent. Option D, \(20x\), does not match the original expression either. Thus, only option A is correct.
To determine the equivalent expression for \(12x + 8\), we can factor out the greatest common factor, which is 4. Option A, \(4(3x + 2)\), simplifies to \(12x + 8\) when distributed, making it equivalent to the original expression. Option B, \(4(3x + 8)\), simplifies to \(12x + 32\), which is not equivalent. Option C, \(4(3x + 2x)\), simplifies to \(4(5x)\) or \(20x\), which is also not equivalent. Option D, \(20x\), does not match the original expression either. Thus, only option A is correct.
If an item regularly costs d dollars and is discounted 12 percent, which of the following represents the discounted price in dollars?
- A. 0.12d
- B. 0.88d
- C. 1.12d
- D. d-0.12
Correct Answer & Rationale
Correct Answer: B
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.
To find the discounted price after a 12 percent discount on an item that costs d dollars, we first calculate the amount of the discount, which is 12% of d, or 0.12d. To determine the final price, we subtract this discount from the original price: d - 0.12d = 0.88d. Option A (0.12d) represents only the discount amount, not the final price. Option C (1.12d) incorrectly suggests an increase in price. Option D (d - 0.12) does not account for the percentage; it inaccurately represents the discount as a flat dollar amount rather than a percentage of the original price. Thus, 0.88d correctly reflects the discounted price.