Final answer:
Without specific details about the relationship between the number of pounds and the cost, it is not possible to definitively answer whether these quantities vary directly or inversely. Direct variation involves both variables increasing or decreasing together, while inverse variation means one variable increases as the other decreases.
Step-by-step explanation:
To determine whether the quantities (the number of pounds and the cost) vary directly or inversely, it is important to understand what each of these terms means in relation to two variables.
Two quantities vary directly when they increase or decrease in the same proportion. This means that as one quantity increases, the other increases at a consistent rate, and the same is true when they decrease. Graphically, this is represented by a straight line with a positive slope when plotted on a graph with specific numbers on the price and quantity axis.
On the other hand, two quantities vary inversely when one quantity increases while the other decreases in such a way that their product is constant. According to Newton's Second Law of Motion, which is a completely different context, if you are seeking an example of inverse proportionality, it would be when force remains constant, and as the mass increases, acceleration decreases. But in this case, we are referring to the relationship between price and quantity.
Options for Proportionality
- Direct Proportionality: When one variable increases, the other variable also increases by the same factor.
- Inverse Proportionality: When one variable increases, the other variable decreases by the same factor.
Because the information provided does not include specific details about the relationship between the number of pounds and cost, it is not possible to conclusively answer whether they are in direct or inverse proportion without those specifics. If you have more details, such as data points or a graph, these could indicate which type of proportional relationship exists between the two quantities.