Question
Charlotte's grandmother gave her money to shop for souvenirs while on vacation. She decides to purchase keychains for her friends.
There is a linear relationship between the number of keychains Charlotte buys and the amount of money in her wallet.
Describe the rate of change for this relationship.
The amount of money in Charlotte's wallet
by
per keychain.
There is a linear relationship between the number of keychains Charlotte buys and the amount of money in her wallet.
Describe the rate of change for this relationship.
The amount of money in Charlotte's wallet
by
per keychain.
Answers
GPT-4o mini
In this scenario, the linear relationship between the number of keychains Charlotte buys and the amount of money in her wallet can be described by the concept of "rate of change." The rate of change represents how much the dependent variable (in this case, the amount of money left in her wallet) changes as the independent variable (the number of keychains bought) increases.
Let's denote:
- \( M \) as the amount of money in Charlotte's wallet.
- \( K \) as the number of keychains purchased.
- \( P \) as the price per keychain.
If Charlotte spends \( P \) dollars on each keychain, the relationship can be expressed mathematically:
\[
M = M_0 - P \cdot K
\]
Here, \( M_0 \) is the initial amount of money Charlotte has, and as she buys more keychains (increasing \( K \)), her total money \( M \) decreases.
The rate of change of the amount of money in her wallet with respect to the number of keychains bought is:
\[
\text{Rate of Change} = -P
\]
This means that for every keychain Charlotte buys, the amount of money in her wallet decreases by the price of one keychain (\( P \)). The negative sign indicates that the amount of money decreases as the number of keychains increases.
In summary, the rate of change of the amount of money in Charlotte's wallet is \(-P\) dollars per keychain, where \( P \) is the price of a single keychain.
Let's denote:
- \( M \) as the amount of money in Charlotte's wallet.
- \( K \) as the number of keychains purchased.
- \( P \) as the price per keychain.
If Charlotte spends \( P \) dollars on each keychain, the relationship can be expressed mathematically:
\[
M = M_0 - P \cdot K
\]
Here, \( M_0 \) is the initial amount of money Charlotte has, and as she buys more keychains (increasing \( K \)), her total money \( M \) decreases.
The rate of change of the amount of money in her wallet with respect to the number of keychains bought is:
\[
\text{Rate of Change} = -P
\]
This means that for every keychain Charlotte buys, the amount of money in her wallet decreases by the price of one keychain (\( P \)). The negative sign indicates that the amount of money decreases as the number of keychains increases.
In summary, the rate of change of the amount of money in Charlotte's wallet is \(-P\) dollars per keychain, where \( P \) is the price of a single keychain.