Use the information given to awnser questions 21-22

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 reward customers with tickets dispersed at regular intervals while playing each game.
21. The equation A9g)=15-0.50g represents the amount of money remaining, A, on customers card after playing g games which statement is true?
A. The intial 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 cost $0.50.
C.The initial amount on the card is $50, and $0.50 is earned for each game.
D.The initl amount on the card is $50, and each game cost $0.15.
22.A customer starts with some tickets, plays the same game multiple times, and receives on average, the same number of tickets for each play of the game. The equation T(x)=25+15/2x re-resents the total number of tickets the customer has after x plays.
Which statement is true?
A.the customer starts with 25 tickets and earns and average of 2 tickets for every 15 plays
B. The customer starts with 25 tickets and earns an average of 15 tickets for every 2 plays.
C. the customer starts with 25 tickets and loses an average of 2 tickets for every 15 plays
D.The customer starts with 25 tickets and loses an average of 15 tickets for every 2 plays

Answer 1

Let's analyze each question based on the equations provided.

21. Analyzing the equation \( A(g) = 15 - 0.50g \):

• This equation represents the amount of money remaining on the card after playing \( g \) games.
• The initial amount on the card is represented by the constant term, which is $15.
• The term \(-0.50g\) indicates that for each game played, the customer spends $0.50.

The correct interpretation is: B. The initial amount on the card is $15 and each game costs $0.50.

22. Analyzing the equation \( T(x) = 25 + \frac{15}{2}x \):

• In this equation, the constant term \( 25 \) represents the initial number of tickets the customer starts with.
• The term \(\frac{15}{2}x\) indicates how many tickets the customer earns based on the number of plays \( x \). Specifically, this means for every 2 plays, the customer earns 15 tickets.

To clarify:

• The average earnings per play can be calculated as \( \frac{15}{2} \) tickets for every 2 plays, which simplifies to \( \frac{15}{2} \div 2 = \frac{15}{4} = 3.75 \) tickets per play.

Given that the customer starts with 25 tickets and earns an average of 15 tickets for every 2 plays, the correct answer is: B. The customer starts with 25 tickets and earns an average of 15 tickets for every 2 plays.

So the final answers are: 21. B 22. B