Eric has $27.00 and wants to buy comic books. If each comic book costs $4.00, create a table and graph the arithmetic sequence to display how much money Eric has left after each comic book purchase. Which graph is an accurate representation of the problem?(1 point)

Responses

1 answer

To create a table and graph representing how much money Eric has left after each comic book purchase, we start with the initial amount Eric has and the cost of each comic book.

Step 1: Create a Table

Let's define the variables:

  • Initial amount: \( A = 27.00 \)
  • Cost of each comic book: \( C = 4.00 \)
  • Number of comic books bought: \( n \)

The money Eric has left after each purchase can be calculated using the formula: \[ \text{Money Left} = A - n \times C \]

Now, let's fill out the table for different values of \( n \) (number of comic books purchased):

| Number of Comic Books (n) | Money Left ($) | |---------------------------|---------------------| | 0 | \( 27.00 - 0 \times 4.00 = 27.00 \) | | 1 | \( 27.00 - 1 \times 4.00 = 23.00 \) | | 2 | \( 27.00 - 2 \times 4.00 = 19.00 \) | | 3 | \( 27.00 - 3 \times 4.00 = 15.00 \) | | 4 | \( 27.00 - 4 \times 4.00 = 11.00 \) | | 5 | \( 27.00 - 5 \times 4.00 = 7.00 \) | | 6 | \( 27.00 - 6 \times 4.00 = 3.00 \) | | 7 | \( 27.00 - 7 \times 4.00 = -1.00 \) |

Step 2: Graph the Sequence

Now, let's plot the data:

  • On the x-axis, we'll represent the number of comic books purchased (n).
  • On the y-axis, we'll represent the money left ($).

Step 3: Create the Graph

  • Points to plot:
    • (0, 27)
    • (1, 23)
    • (2, 19)
    • (3, 15)
    • (4, 11)
    • (5, 7)
    • (6, 3)
    • (7, -1)

Resulting Graph

The resulting graph will show a decreasing linear trend starting from (0, 27) and sloping downwards to (7, -1). The line will be straight, as Eric loses a constant amount ($4.00) for each comic book purchased.

Conclusion

When interpreting the graph, make sure it clearly shows the correlation between the number of comic books purchased and the money left. If there are multiple graph options provided, look for the one that accurately reflects a linear decreasing line that starts at 27 and decreases towards -1 as n increases.

If further visuals or actual graphs were provided in responses, choose the one that matches this explanation.