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Jim and his friends are at an arcade and are redeeming their tickets for prizes. The number of tickets they have won determines how many prizes they can get. $\newline$ $t =$ the number of tickets the friends have won $\newline$ $p =$ the number of prizes the friends can get $\newline$ Which of the variables is independent and which is dependent? $\newline$ Choices: $\newline$ (A) $p$ is the independent variable and $t$ is the dependent variable $\newline$ (B) $t$ is the independent variable and $p$ is the dependent variable

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Identify independent and dependent variables

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Q. Jim and his friends are at an arcade and are redeeming their tickets for prizes. The number of tickets they have won determines how many prizes they can get.

\newline

t =

the number of tickets the friends have won

\newline

p =

the number of prizes the friends can get

\newline

Which of the variables is independent and which is dependent?

\newline

Choices:

\newline

(A)

p

is the independent variable and

t

is the dependent variable

\newline

(B)

t

is the independent variable and

p

is the dependent variable

Define Variables: In any function or relationship between two variables, the independent variable is the one that is chosen or controlled by the participants, and the dependent variable is the one that depends on the independent variable. In this context, the number of tickets won $t$ is what Jim and his friends have control over by playing games. The number of prizes they can get $p$ depends on the number of tickets they have. Therefore, the number of tickets $t$ is the independent variable, and the number of prizes $p$ is the dependent variable.
Identify Independent and Dependent: Now, let's look at the choices given to determine which one correctly identifies the independent and dependent variables. $\newline$ (A) $p$ is the independent variable and $t$ is the dependent variable $\newline$ (B) $t$ is the independent variable and $p$ is the dependent variable $\newline$ Based on our reasoning in the previous step, we can see that choice (B) correctly identifies $t$ as the independent variable and $p$ as the dependent variable.

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