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?
A. The initial amount on the card is $15, and $0.50 is earned for each game.
B. The initial amount on the card is $15, and each game costs $0.50.
C. The initial amount on the card is $50, and $0.50 is earned for each game.
D. The initial amount on the card is $50, and each game costs $0.15.
The equation π¨(π) = ππ β π. πππ represents the amount of money remaining, π¨, on a customerβs card after playing π games.
To determine the initial amount on the card, we need to substitute π=0 into the equation π¨(π) = ππ β π. πππ and solve for π΄.
When π=0, π¨(0) = ππ β π. ππ(0)
Simplifying, π¨(0) = ππ β π
Therefore, the initial amount on the card is $15.
To determine the amount earned or spent per game, we need to determine the change in the amount after one game. We can do this by subtracting the amount after one game from the initial amount.
π¨(1) = ππ β π. ππ(1)
Simplifying, π¨(1) = ππ β π. ππ
Therefore, each game costs $0.50.
The correct statement is:
B. The initial amount on the card is $15, and each game costs $0.50.
To determine which statement is true, let's analyze the given equation π¨(π) = ππ β π. πππ.
In the equation, π¨(π) represents the amount of money remaining on the customer's card after playing π games.
We can break down the equation as follows:
- The initial amount on the card is denoted by π¨.
- For each game played, an amount of money is deducted from the card. Since the coefficient of π in the equation is -0.50, it means $0.50 is deducted from the card after each game is played.
Based on this analysis, we can conclude that statement B is true:
B. The initial amount on the card is $15, and each game costs $0.50.
To determine the correct answer, let's break down the given equation π¨(π) = ππ β π. πππ.
In the equation, π¨ represents the amount of money remaining on the customer's card, and π represents the number of games played. The equation is trying to calculate how much money is left on the card after playing a certain number of games.
Let's start by examining the constants in the equation. The number 15 represents the initial amount on the card, which is the starting point before any games are played.
The coefficient (-0.50π) represents the amount of money earned or deducted with each game played. Since the coefficient is negative (-0.50π), it means that money is being deducted from the card with each game played.
Now, let's compare the given options with the equation to find the correct statement:
A. The initial amount on the card is $15, and $0.50 is earned for each game.
This option conflicts with the equation since the coefficient (-0.50π) indicates money is being deducted with each game played, not earned.
B. The initial amount on the card is $15, and each game costs $0.50.
This option matches the equation since the coefficient (-0.50π) represents the cost of each game.
C. The initial amount on the card is $50, and $0.50 is earned for each game.
This option conflicts with the equation since the initial amount on the card is given as $50, which is different from the given equation's starting point of $15.
D. The initial amount on the card is $50, and each game costs $0.15.
This option conflicts with the equation since the coefficient (-0.50π) is different from the given cost per game of $0.15.
Therefore, the correct statement is option B: The initial amount on the card is $15, and each game costs $0.50.