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.