Question
An arcade offers customers the option to put money on pre-paid cards and then swipe their cards to pay for each game played. Games also award customers with tickets dispersed at regular intervals while playing each game.
The equation π¨(π) = ππ β π. πππ represents the amount of money remaining, π¨, on a customerβs card after playing π games. Which statement is true?
The equation π¨(π) = ππ β π. πππ represents the amount of money remaining, π¨, on a customerβs card after playing π games. Which statement is true?
Answers
GPT-4o mini
To analyze the equation \( A(g) = 15 - 0.50g \), let's break down its components:
- \( A(g) \) represents the amount of money remaining on the card after playing \( g \) games.
- The initial amount on the card is $15.
- For each game played, the customer spends $0.50 (since playing \( g \) games costs \( 0.50g \)).
We can derive several insights from this equation:
1. **Initial Amount:** When \( g = 0 \) (no games played), the amount remaining on the card is \( A(0) = 15 - 0.50(0) = 15 \). So, the initial amount on the card is $15.
2. **Cost per Game:** Each game played reduces the amount of money on the card by $0.50. Therefore, the total cost for \( g \) games is \( 0.50g \).
3. **Limit:** The function \( A(g) \) represents a linear decrease in the amount of money on the card. If the customer plays enough games (specifically when \( A(g) \) reaches $0), they will run out of money on the card. To find out how many games that would take, we can set the equation to zero:
\[
15 - 0.50g = 0
\]
Solving for \( g \):
\[
0.50g = 15 \\
g = \frac{15}{0.50} = 30
\]
This means the customer can play a maximum of 30 games before the card balance reaches $0.
4. **Interpretation of \( A(g) \):** The equation shows that the amount remaining on the card decreases linearly with the number of games played, confirming the expenditure of money per game.
Based on this analysis, **the true statement** regarding this equation is: **The customer can play 30 games before their card balance reaches $0.**
- \( A(g) \) represents the amount of money remaining on the card after playing \( g \) games.
- The initial amount on the card is $15.
- For each game played, the customer spends $0.50 (since playing \( g \) games costs \( 0.50g \)).
We can derive several insights from this equation:
1. **Initial Amount:** When \( g = 0 \) (no games played), the amount remaining on the card is \( A(0) = 15 - 0.50(0) = 15 \). So, the initial amount on the card is $15.
2. **Cost per Game:** Each game played reduces the amount of money on the card by $0.50. Therefore, the total cost for \( g \) games is \( 0.50g \).
3. **Limit:** The function \( A(g) \) represents a linear decrease in the amount of money on the card. If the customer plays enough games (specifically when \( A(g) \) reaches $0), they will run out of money on the card. To find out how many games that would take, we can set the equation to zero:
\[
15 - 0.50g = 0
\]
Solving for \( g \):
\[
0.50g = 15 \\
g = \frac{15}{0.50} = 30
\]
This means the customer can play a maximum of 30 games before the card balance reaches $0.
4. **Interpretation of \( A(g) \):** The equation shows that the amount remaining on the card decreases linearly with the number of games played, confirming the expenditure of money per game.
Based on this analysis, **the true statement** regarding this equation is: **The customer can play 30 games before their card balance reaches $0.**