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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 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.

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 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.

1 answer

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

  1. Identify the total weight limit: The maximum weight of the elevator is 2,000 pounds.

  2. Account for Lionel's weight: Lionel weighs 170 pounds, so we must subtract his weight from the total weight limit to determine the weight limit for the boxes: \[ \text{Weight limit for boxes} = \text{Total weight limit} - \text{Lionel's weight} = 2000 - 170 = 1830 \text{ pounds} \]

  3. Determine the weight per box: Since there are 10 boxes, we can divide the total weight limit for the boxes by the number of boxes to find the maximum weight each box can hold: \[ \text{Maximum weight per box} = \frac{\text{Weight limit for boxes}}{\text{Number of boxes}} = \frac{1830}{10} = 183 \text{ pounds} \]

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

Graphing the Solution

Since we found that each box can weigh up to 183 pounds, we can show this on a number line:

  • The number line should range from 0 to at least 200 pounds (or more if specified).
  • We would plot a closed point at 183 and then indicate that boxes can weigh anywhere from 0 up to 183 pounds but not more.

Final Representation:

  • A closed point at 183 on the number line with a line extending to the left (indicating weights from 0 to 183 pounds).

Based on the options provided, the correct representation corresponds to the one that shows a closed point at 183 with a line extending to the right beyond 300 pounds, indicating that boxes can weigh up to 183 pounds and there is no restriction on weights greater than that point.

Correct answer: 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.