Question

The cost of one pencil is $3, and the total cost of three pencils is $9. Which of the following is true?
A.
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.
B.
The number of pencils and the total cost are in a proportional relationship because the cost increases with the number of pencils.
C.
The number of pencils and the total cost are in a proportional relationship because the cost does not increase 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 costs $3.

Answer 1

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.