Ling is an avid runner who purchases a new pair of running shoes every $300$ miles. The number of pairs of shoes Ling buys each year depends on how many miles she runs in that year. $\newline$ $p =$ the number of pairs of shoes Ling buys in a year $\newline$ $m =$ the number of miles Ling runs in a year $\newline$ Which of the variables is independent and which is dependent? $\newline$ Choices: $\newline$ (A) $p$ is the independent variable and $m$ is the dependent variable $\newline$ (B) $m$ is the independent variable and $p$ is the dependent variable

Full solution

Q. Ling is an avid runner who purchases a new pair of running shoes every

300

miles. The number of pairs of shoes Ling buys each year depends on how many miles she runs in that year.

\newline

p =

the number of pairs of shoes Ling buys in a year

\newline

m =

the number of miles Ling runs in a year

\newline

Which of the variables is independent and which is dependent?

\newline

Choices:

\newline

(A)

p

is the independent variable and

m

is the dependent variable

\newline

(B)

m

is the independent variable and

p

is the dependent variable

Identify Variable Type: Identify whether $p$ is the independent or the dependent variable. The number of pairs of shoes Ling buys is determined by how many miles she runs. Therefore, $p$ is not independent of $m$ ; instead, it depends on the value of $m$ .
Determine Relationship: Identify whether $m$ is the independent or the dependent variable. The number of miles Ling runs does not depend on how many pairs of shoes she buys. Therefore, $m$ is the independent variable because it is the variable that is controlled by Ling's actions, not by the number of shoes she has.
Express Relationship: Determine the relationship between $p$ and $m$ . Since Ling buys a new pair of shoes every $300$ miles, the number of pairs of shoes $p$ she buys is directly proportional to the number of miles $m$ she runs. We can express this relationship as $p = \frac{m}{300}$ .
Choose Correct Answer: Choose the correct answer choice based on the identification of independent and dependent variables. Since $m$ is the independent variable and $p$ is the dependent variable, the correct choice is (B) $m$ is the independent variable and $p$ is the dependent variable.