One online movie-streaming service costs $8 per month and charges $1.50 per movie. A second service costs $2 per month and charges $2 per movie. For what number of movies per month is the monthly cost of both services the same?
- A. 3
- B. 6
- C. 5
- D. 12
- E. 20
Correct Answer & Rationale
Correct Answer: D
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
Other Related Questions
The distance from Earth to the sun is approximately 9×10ⷠmiles. The diameter of Earth is approximately 8,000 miles. The distance from Earth to the sun is approximately how many times the diameter of Earth?
- A. 1000
- B. 9000
- C. 11000
- D. 90000
- E. 9000000
Correct Answer & Rationale
Correct Answer: C
To determine how many times the diameter of Earth fits into the distance from Earth to the sun, we divide the distance (9×10^7 miles) by Earth's diameter (8,000 miles). Calculating: 9×10^7 miles ÷ 8,000 miles = 11,250. This rounds down to approximately 11,000, making option C the closest answer. Option A (1000) significantly underestimates the distance. Option B (9000) is also too low, while option D (90000) and option E (9000000) greatly overestimate the number of times the diameter fits into the distance. Thus, C is the most accurate choice.
To determine how many times the diameter of Earth fits into the distance from Earth to the sun, we divide the distance (9×10^7 miles) by Earth's diameter (8,000 miles). Calculating: 9×10^7 miles ÷ 8,000 miles = 11,250. This rounds down to approximately 11,000, making option C the closest answer. Option A (1000) significantly underestimates the distance. Option B (9000) is also too low, while option D (90000) and option E (9000000) greatly overestimate the number of times the diameter fits into the distance. Thus, C is the most accurate choice.
A home improvement store offers to finance the purchase of any single item with zero interest for one year, with a down payment of $50. The remainder of the purchase price will be split into 12 equal monthly payments. Which of the following equations represents the relationship between an item's purchase price, s dollars, and the amount, a dollars, of each monthly payment under this offer?
- A. s = a-50/12
- B. s = a/12 -50
- C. s = 12a + 50
- D. s = 12a - 50
- E. s = 12 (a + 50)
Correct Answer & Rationale
Correct Answer: C
To determine the relationship between the item's purchase price \( s \) and the monthly payment \( a \), consider the financing terms. After a $50 down payment, the remaining amount to finance is \( s - 50 \). This amount is divided into 12 equal monthly payments, leading to the equation \( s - 50 = 12a \). Rearranging this gives \( s = 12a + 50 \), confirming option C. Options A and B misrepresent the relationship by incorrectly adjusting the down payment or monthly payments. Option D incorrectly subtracts the down payment from the total, while option E miscalculates the total by incorrectly adding the down payment to the monthly payment before multiplying.
To determine the relationship between the item's purchase price \( s \) and the monthly payment \( a \), consider the financing terms. After a $50 down payment, the remaining amount to finance is \( s - 50 \). This amount is divided into 12 equal monthly payments, leading to the equation \( s - 50 = 12a \). Rearranging this gives \( s = 12a + 50 \), confirming option C. Options A and B misrepresent the relationship by incorrectly adjusting the down payment or monthly payments. Option D incorrectly subtracts the down payment from the total, while option E miscalculates the total by incorrectly adding the down payment to the monthly payment before multiplying.
Quadrilateral ABCD satisfies the following conditions: Side AB is parallel to side CD, Side BC is not parallel to side AD. Which term is the best classification for quadrilateral ABCD?
- A. Parallelogram
- B. Rectangle
- C. Rhombus
- D. Square
- E. Trapezoid
Correct Answer & Rationale
Correct Answer: E
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
- A. 524
- B. 2240
- C. 2760
- D. 5000
- E. 12000
Correct Answer & Rationale
Correct Answer: C
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.