Each month, the charge for a lawn care service consists of a flat fee of $25, plus $5 each time the lawn is mowed. Which of the following equations represents the total monthly charge, A(m), in dollars, as a function of the number of times the lawn is mowed, m?
- A. A(m) = 5(25)m
- B. A(m) = 5 + 25m
- C. A(m) = 5m + 25
- D. A(m) = 25m + 5
- E. A(m) = m + 5 + 25
Correct Answer & Rationale
Correct Answer: C
The equation A(m) = 5m + 25 accurately represents the total monthly charge for the lawn care service. Here, the term 5m accounts for the $5 charge per mowing, and the flat fee of $25 is added to this total. Option A incorrectly multiplies the flat fee by the number of mowings, which misrepresents the structure of the charges. Option B misplaces the flat fee, summing it with the number of mowings instead of adding it as a fixed cost. Option D incorrectly places the flat fee as a coefficient of m, which distorts the relationship. Option E combines the charges incorrectly, failing to clearly separate the flat fee from the per-mow charge.
The equation A(m) = 5m + 25 accurately represents the total monthly charge for the lawn care service. Here, the term 5m accounts for the $5 charge per mowing, and the flat fee of $25 is added to this total. Option A incorrectly multiplies the flat fee by the number of mowings, which misrepresents the structure of the charges. Option B misplaces the flat fee, summing it with the number of mowings instead of adding it as a fixed cost. Option D incorrectly places the flat fee as a coefficient of m, which distorts the relationship. Option E combines the charges incorrectly, failing to clearly separate the flat fee from the per-mow charge.
Other Related Questions
Through which pair of points could a line of best fit be drawn for the data on the scatterplot?
- A. (0, 36) and (11, 74)
- B. (1, 39) and (6, 60)
- C. (5, 50) and (6, 60)
- D. (6, 60) and (8, 60)
- E. (8, 60) and (11, 74)
Correct Answer & Rationale
Correct Answer: A
Option A, with points (0, 36) and (11, 74), shows a significant range in both x and y values, indicating a strong upward trend that aligns well with the overall direction of the data. Option B, while showing an upward trend, has a narrower range and may not represent the overall data as effectively. Option C features two points that are too close together, limiting their ability to define a clear line of best fit. Option D includes points with the same y-value, suggesting a horizontal line that does not capture the data's trend. Option E, like A, has a valid upward trend but does not span the data range as effectively as A.
Option A, with points (0, 36) and (11, 74), shows a significant range in both x and y values, indicating a strong upward trend that aligns well with the overall direction of the data. Option B, while showing an upward trend, has a narrower range and may not represent the overall data as effectively. Option C features two points that are too close together, limiting their ability to define a clear line of best fit. Option D includes points with the same y-value, suggesting a horizontal line that does not capture the data's trend. Option E, like A, has a valid upward trend but does not span the data range as effectively as A.
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.
A bowl contains 18 pieces of candy: 8 red, 6 orange, and 4 green. Brandon will select 1 piece of candy at random. What is the probability that Brandon will select a green piece?
- A. 2/7
- B. 2/9
- C. 2/11
- D. 1/9
- E. 1/8
Correct Answer & Rationale
Correct Answer: B
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
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.