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Lionel is loading boxes of books into an elevator to move to the 35th floor of an office building. There are 10 boxes of books, and Lionel wants to make sure he is not exceeding the maximum weight of the elevator, which is 2,000 pounds. Lionel weighs 170 pounds. If each box of books weighs the same amount, how much can each box weigh? Solve this problem and then graph the solution on a number line.(1 point)
Responses

An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 50 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 200.
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 50 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 200.

An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 50 to 300 in 50 unit increments. A closed point is plotted at 183. A line extends from that point to the right and goes beyond 300.
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 50 to 300 in 50 unit increments. A closed point is plotted at 183. A line extends from that point to the right and goes beyond 300.

An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 50 to 300 in 50 unit increments. A closed point is plotted at 200. A line extends from that point to the right and goes beyond 300.
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 50 to 300 in 50 unit increments. A closed point is plotted at 200. A line extends from that point to the right and goes beyond 300.

An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 20 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 183.
Image with alt text: An illustration shows a number line labeled Weight of Each Box in the Elevator. The number line ranges from 0 to 200 in 20 unit increments. A closed point is plotted at 0. A line extends from that point to the right, connecting with a closed point at 183.
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1 answer

To solve the problem, we need to determine the maximum weight each box of books can have without exceeding the elevator's weight limit.

  1. Determine the total weight limit of the elevator:

    • The maximum weight of the elevator = 2,000 pounds
    • Lionel's weight = 170 pounds

  2. Calculate the weight available for the boxes: \[ \text{Weight available for boxes} = \text{Maximum weight of the elevator} - \text{Lionel's weight} = 2,000 - 170 = 1,830 \text{ pounds} \]

  3. Determine how much each box can weigh:

    • Lionel has 10 boxes of books.
    • Let \( x \) be the weight of each box.
    • Therefore, the total weight of the boxes is \( 10x \).

    We need to ensure that the total weight of the boxes does not exceed the available weight: \[ 10x \leq 1,830 \]

    Dividing both sides by 10 gives: \[ x \leq \frac{1,830}{10} = 183 \text{ pounds} \]

Thus, each box of books can weigh a maximum of 183 pounds.

  1. Graph the solution: The solution indicates that the weight of each box can be anywhere from 0 to 183 pounds, inclusive. On a number line, this can be depicted as follows:
  • The number line ranges from 0 to 200.
  • A closed point is plotted at 0, and a closed point is plotted at 183.
  • A solid line connects these two points to show all possible weights for each box.

Based on this analysis, the correct response is the illustration that shows a number line labeled "Weight of Each Box in the Elevator," ranging from 0 to 200 in which a closed point is at 0 and a solid line extends to 183.

Thus, the last description mentioning a range from 0 to 200, with a closed point at 0 and extending to a closed point at 183, represents the answer correctly. This option is the fourth choice based on the provided descriptions.