Question

You buy some oranges for \(\$.80\) per pound. Which direct variation model relates the total cost x to the number of pounds of oranges y? (A) \(y=8 x\) (B) \(x=0.8 y\) (C) \(y=0.8 x\) (D) \(x=8 y\)

Short answer

The direct variation model that relates the total cost x to the number of pounds of oranges y is \(x = 0.8y\) (Option B).

Step-by-step solution

Identify the Variables

The problem states that the total cost is represented by variable x and the number of pounds of oranges is represented by variable y.

Recognize the Direct Variation Relationship

We know in a direct variation relationship, one variable is a constant multiple of the other. In this case, the total cost (x) is the amount of oranges we buy (y) times the cost per pound (which is \$.80). So we can write this relationship as \(x = 0.8y\).

Choose the Correct Option

Now, we can see which of the given options matches the direct variation relationship that we have just derived. The correct model is \(x = 0.8y\).