A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?

The value of x can be any real number, and y will be a real number.
The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0.
The value of x can be any integer, and y will be an integer.
The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.

1 answer

To understand the relationship between the number of notebooks Adele buys (represented by \( x \)) and the total cost of the notebooks (represented by \( y \)), we need to consider the pricing details provided:

  1. Each notebook costs $3.
  2. There is no sales tax.

The total cost \( y \) can be calculated using the formula: \[ y = 3x \]

Now, let's analyze the possible values of \( x \) and \( y \):

  • For \( x \): Since Adele can buy a certain number of notebooks, \( x \) must be a non-negative integer (it’s not possible to buy a negative number of notebooks, and it must also be a whole number since you cannot buy a fraction of a notebook).

  • For \( y \): Since \( y \) is calculated as \( y = 3x \), and \( x \) can be a non-negative integer starting from \( 0 \), then \( y \) will also be a non-negative integer (specifically, \( 0, 3, 6, 9, \ldots \)).

Given that both \( x \) and \( y \) can only take values that are whole numbers and non-negative, the best description of the values of \( x \) and \( y \) is:

The value of \( x \) can be any integer greater than or equal to 0, and \( y \) will be an integer greater than or equal to 0.

So the correct answer is: The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.