The cost of one pencil is three dollars The total cost of three pencils is nine dollars. Which of the following is true.
A.the number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils
B. The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is 0$ and it does not increase proportionally with the number of pencils
C.the number of pencils and the total cost are in a proportional relationship because the cost increases with the number of pencils
D.the number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is 0$ and each pencil cost 3$
B. The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is 0$ and it does not increase proportionally with the number of pencils.
The correct answer is B. The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0 and it does not increase proportionally with the number of pencils. In this scenario, each pencil costs $3, so if we have 3 pencils, the total cost would be $9.
To determine the correct answer, we need to understand the concept of proportionality. In a proportional relationship, when one quantity increases or decreases, the other quantity changes in direct proportion.
Let's analyze the options:
A. The number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils.
The cost of one pencil is three dollars, and the total cost of three pencils is nine dollars. In this scenario, the cost does increase with the number of pencils. Since option A states that the cost does not increase with the number of pencils, it is not true.
B. The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0, and it does not increase proportionally with the number of pencils.
Option B correctly states that the cost of zero pencils is $0, which aligns with the definition of proportionality. However, it is essential to consider the term "proportionally." In a proportional relationship, the cost should increase proportionally with the number of pencils. Since the cost of one pencil is $3, and the total cost of three pencils is $9, the cost increases proportionally. Therefore, option B is not entirely accurate.
C. The number of pencils and the total cost are in a proportional relationship because the cost increases with the number of pencils.
Option C describes the situation accurately. As the number of pencils increases from one to three, the total cost increases from $3 to $9, indicating a proportional relationship.
D. The number of pencils and the total cost are in a proportional relationship because the cost of zero pencils is $0, and each pencil costs $3.
Option D acknowledges the fact that the cost of zero pencils is $0, which supports proportionality. It also correctly states that each pencil costs $3. Therefore, option D accurately describes the relationship between the number of pencils and the total cost.
Based on the analysis, the correct answer is option D.