Question

Critique Reasoning: You spend d dollars

for g identical pairs of glasses. A friend claims
that because d increases if you increase g,
and g increases if you increase d, either d or
g could be the independent variable. Is your
friend correct? Explain.

Answer 1

Answer: In this situation, it is not correct to say that either d or g could be the independent variable.

Step-by-step explanation: In this scenario g is the independent variable and d is the dependent variable.

The independent variable is the variable that is being intentionally manipulated or changed in an experiment or analysis, while the dependent variable is the variable that is being measured or observed. In this case, it is clear that the quantity of glasses (g) is the independent variable because it is being intentionally varied in order to observer the corresponding changes in the cost (d).

While it is true that d and g are related (e.g., increasing g will result in an increase in d), this does not imply that d could be the independent variable. This is because changes in d are a consequence of changes in g, not the other way around.

Answer 2

The reasoning of the friend is incorrect. The independent variable is manipulated or changed in an experiment, while the dependent variable is the unstable being measured. In this case, the independent variable is the number of identical pairs of glasses, g, since it is the variable being changed. The dependent variable is the amount of money spent, d since it is the variable being measured.

Therefore, increasing g causes an increase in d, which means that d is dependent on g, and g is independent of d. Consequently, it is crucial to correctly identify an experiment's independent and dependent variables to ensure accurate and meaningful results.

Explanation: