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Carl sells snow cones at a baseball park. The graph shows the amount of ice used for the snow cones, in pounds, over a certain amount of time, in minutes.

graph titled snow cone stand with the x-axis labeled time in minutes and the y-axis labeled amount of ice for cones in pounds with a line segment from 0 comma 0 to 2 comma 8 and a horizontal line segment from 2 comma 8 to 6 comma 8 and another segment from 6 comma 8 to 12 comma 5

Which of the following describes the graph?
Carl had 1 pound of ice after 2 minutes, used 8 pounds every minute for 4 minutes, and then used 3 pounds each minute for 6 minutes.
Carl had 2 pounds of ice after 8 minutes, used 8 pounds every minute for 4 minutes, and then used one half pound each minute for 6 minutes.
Carl had 4 pounds of ice after 1 minute, didn't use any ice for 4 minutes, and then used 2 pounds each minute for 6 minutes.
Carl had 8 pounds of ice after 2 minutes, didn't use any ice for 4 minutes, and then used one half pound each minute for 6 minutes.

1 answer

Let's analyze the graph you described:

  1. The first line segment from \( (0, 0) \) to \( (2, 8) \) indicates that in the first 2 minutes, Carl used 8 pounds of ice. Since this is a straight line, it implies a constant rate of usage. To find the rate, we compute the change in ice amount over time:

    • From \( 0 \) pounds to \( 8 \) pounds over \( 2 \) minutes means he used \( \frac{8 - 0}{2 - 0} = 4 \) pounds per minute.

  2. The horizontal line segment from \( (2, 8) \) to \( (6, 8) \) indicates that from 2 to 6 minutes (a duration of 4 minutes), the amount of ice remains constant at 8 pounds. This indicates that Carl did not use any ice during this period.

  3. The final segment from \( (6, 8) \) to \( (12, 5) \) indicates that from minute 6 to minute 12, he used ice to go from 8 pounds to 5 pounds, which means he used 3 pounds of ice over 6 minutes. His rate of ice usage during this period is:

    • From \( 8 \) pounds to \( 5 \) pounds over \( 6 \) minutes implies a usage of \( \frac{5 - 8}{12 - 6} = \frac{-3}{6} = -0.5 \) pounds per minute.

Now, let's evaluate the options provided:

  1. Carl had 1 pound of ice after 2 minutes, used 8 pounds every minute for 4 minutes, and then used 3 pounds each minute for 6 minutes.

    • This is incorrect. He had 8 pounds after 2 minutes, not 1 pound, and he didn't use 8 pounds every minute for 4 minutes.

  2. Carl had 2 pounds of ice after 8 minutes, used 8 pounds every minute for 4 minutes, and then used one half pound each minute for 6 minutes.

    • This is also incorrect because he had 5 pounds after 12 minutes, and he did not use 8 pounds every minute for 4 minutes.

  3. Carl had 4 pounds of ice after 1 minute, didn't use any ice for 4 minutes, and then used 2 pounds each minute for 6 minutes.

    • This is incorrect because he had 8 pounds after 2 minutes and used ice for 2 minutes.

  4. Carl had 8 pounds of ice after 2 minutes, didn't use any ice for 4 minutes, and then used one half pound each minute for 6 minutes.

    • This option is correct. He did have 8 pounds after 2 minutes, did not use ice for the next 4 minutes (remaining at 8 pounds), and then he used 0.5 pounds per minute for 6 minutes, reducing the amount of ice from 8 pounds to 5 pounds.

Thus, the correct statement that describes the graph is: "Carl had 8 pounds of ice after 2 minutes, didn't use any ice for 4 minutes, and then used one half pound each minute for 6 minutes."