Identify the dependent variable in the following situation: Ethan spent 𝑑 dollars on 𝑛 pens. a) The number of dollars, 𝑑 or b) the number of pens, 𝑛.
Let’s think about this situation in terms of input and output. In this machine, we have an input that we put in, a rule that somehow changes what we’ve put in, and outcomes, the output. The input here represents the independent variable, and the output represents the dependent variable, because the output depends on the rule.
We can use this machine to model our situation. What is the rule here? What is changing? We calculate the money based on the price of the pens. The number of pens, 𝑛, goes into our machine. We calculate the price per pen, and out comes the number of dollars Ethan needs to spend, 𝑑.
The dollars Ethan spends depends on the price of the pens and the number of pens he buys. We were interested in the dependent variable, and that would be option a), the number of dollars, 𝑑. The number of dollars depends on the number of pens and the price of those pens.