Choose the best answer. If necessary, use the paper you were given.
A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay, excluding tax, for the shirt?
- A. 0.15x-5
- B. 0.85x -5
- C. 0.85(x-5)
- D. 5-0.85x
Correct Answer & Rationale
Correct Answer: B
To determine the price a customer pays after applying both discounts, start with the original price, x. A 15% discount reduces the price to 85% of the original, calculated as 0.85x. After this, the customer applies a $5 coupon, leading to the final price of 0.85x - 5. Option A (0.15x - 5) incorrectly calculates the discount as a direct subtraction from the original price, misrepresenting the order of operations. Option C (0.85(x - 5)) mistakenly applies the coupon before calculating the discount, which is not the correct sequence. Option D (5 - 0.85x) suggests a negative price, which is nonsensical in this context.
To determine the price a customer pays after applying both discounts, start with the original price, x. A 15% discount reduces the price to 85% of the original, calculated as 0.85x. After this, the customer applies a $5 coupon, leading to the final price of 0.85x - 5. Option A (0.15x - 5) incorrectly calculates the discount as a direct subtraction from the original price, misrepresenting the order of operations. Option C (0.85(x - 5)) mistakenly applies the coupon before calculating the discount, which is not the correct sequence. Option D (5 - 0.85x) suggests a negative price, which is nonsensical in this context.
Other Related Questions
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.
Which of the following represents the cost, in dollars, of renting a car for d days and driving m miles?
- A. 45+.25+ d+m
- B. 45.25+ dm
- C. 45d +.25m
- D. 45/d +25/m
Correct Answer & Rationale
Correct Answer: C
Option C accurately represents the cost of renting a car, where $45 is a fixed daily rental fee multiplied by the number of days (d) and $0.25 is the cost per mile multiplied by the number of miles driven (m). Option A incorrectly adds the fixed cost and variable costs without proper multiplication, leading to an illogical expression. Option B misrepresents the relationship by multiplying the daily rate by the miles driven, which does not reflect the cost structure. Option D divides the fixed cost by days and the cost per mile by miles, which does not align with standard cost calculations for renting a car.
Option C accurately represents the cost of renting a car, where $45 is a fixed daily rental fee multiplied by the number of days (d) and $0.25 is the cost per mile multiplied by the number of miles driven (m). Option A incorrectly adds the fixed cost and variable costs without proper multiplication, leading to an illogical expression. Option B misrepresents the relationship by multiplying the daily rate by the miles driven, which does not reflect the cost structure. Option D divides the fixed cost by days and the cost per mile by miles, which does not align with standard cost calculations for renting a car.
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%.
The system of equations above has how many solutions? x+4y=3, 2x+8y=4
- A. None
- B. One
- C. Two
- D. Infinitely many
Correct Answer & Rationale
Correct Answer: A
To determine the number of solutions for the system of equations, we first analyze the equations: \(x + 4y = 3\) and \(2x + 8y = 4\). The second equation can be simplified by dividing all terms by 2, resulting in \(x + 4y = 2\). Now, we have two equations: \(x + 4y = 3\) and \(x + 4y = 2\). Since both equations represent parallel lines (same slope, different y-intercepts), they will never intersect, indicating there are no solutions. Option B suggests one solution, which is incorrect as parallel lines do not meet. Option C suggests two solutions, which is also incorrect for the same reason. Option D proposes infinitely many solutions, which applies only to identical lines, not parallel ones. Thus, the system has no solutions.
To determine the number of solutions for the system of equations, we first analyze the equations: \(x + 4y = 3\) and \(2x + 8y = 4\). The second equation can be simplified by dividing all terms by 2, resulting in \(x + 4y = 2\). Now, we have two equations: \(x + 4y = 3\) and \(x + 4y = 2\). Since both equations represent parallel lines (same slope, different y-intercepts), they will never intersect, indicating there are no solutions. Option B suggests one solution, which is incorrect as parallel lines do not meet. Option C suggests two solutions, which is also incorrect for the same reason. Option D proposes infinitely many solutions, which applies only to identical lines, not parallel ones. Thus, the system has no solutions.