Question
Rebecca is selling lemonade by the glass on the first hot day of summer. She plans to donate her profits to the local animal shelter.
There is a linear relationship between the number of glasses of lemonade Rebecca sells and the total amount of money she makes.
Describe the rate of change for this relationship.
The total amount of money Rebecca makes
by
per glass she sells.
There is a linear relationship between the number of glasses of lemonade Rebecca sells and the total amount of money she makes.
Describe the rate of change for this relationship.
The total amount of money Rebecca makes
by
per glass she sells.
Answers
GPT-4o mini
The rate of change for the relationship between the total amount of money Rebecca makes and the number of glasses of lemonade she sells is the price she charges for each glass. This can be described as the amount of money she makes **per glass** she sells.
For example, if Rebecca charges $2 for each glass of lemonade, her total earnings increase by $2 for every additional glass she sells. Therefore, the rate of change is $2 per glass.
In general, this rate of change can be represented as:
**Rate of change = Total Amount Earned / Number of Glasses Sold.**
If she sells \( x \) glasses at \( p \) dollars each, then the total amount of money she makes is represented by the equation:
\[
\text{Total Earnings} = p \cdot x
\]
Thus, the rate of change remains constant as \( p \), which is the price per glass.
For example, if Rebecca charges $2 for each glass of lemonade, her total earnings increase by $2 for every additional glass she sells. Therefore, the rate of change is $2 per glass.
In general, this rate of change can be represented as:
**Rate of change = Total Amount Earned / Number of Glasses Sold.**
If she sells \( x \) glasses at \( p \) dollars each, then the total amount of money she makes is represented by the equation:
\[
\text{Total Earnings} = p \cdot x
\]
Thus, the rate of change remains constant as \( p \), which is the price per glass.