To determine the correct statement regarding the relationship between the number of pencils and the total cost, we need to consider the definition of a proportional relationship. A proportional relationship exists when two quantities have a constant ratio. In this case, for each pencil purchased, the cost increases by a constant amount ($3).
Given:
- Cost of one pencil = $3
- Total cost of three pencils = $9
Using the above information, we can analyze the options:
A. False - This statement incorrectly claims that the cost does not increase proportionally with the number of pencils.
B. True - The cost increases with the number of pencils in a constant manner (each pencil costs $3), indicating a proportional relationship.
C. False - This statement claims that the cost does not increase with the number of pencils, which is incorrect; it does increase.
D. True but requires clarification - While it correctly states that the cost of zero pencils is $0 and each pencil costs $3, more emphasis on the constant relationship (cost increases proportionally) is necessary for a full explanation of proportionality.
The best answer is B, as it directly states that the cost increases with the number of pencils, indicating a proportional relationship.
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