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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)
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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 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 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.
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1 answer

To solve the problem, we first need to determine how much weight Lionel can load into the elevator with the boxes of books.

  1. Find the maximum weight capacity for the boxes: The maximum weight of the elevator is 2,000 pounds. Lionel weighs 170 pounds. \[ \text{Maximum weight for boxes} = \text{Total capacity} - \text{Lionel's weight} \] \[ \text{Maximum weight for boxes} = 2000 - 170 = 1830 \text{ pounds} \]

  2. Determine the maximum weight per box: There are 10 boxes of books, and we want to find out how much each box can weigh. Let \( x \) be the weight of each box. Therefore, the total weight of all boxes is: \[ 10x \] We need this to be less than or equal to 1830 pounds: \[ 10x \leq 1830 \] To find \( x \), divide both sides by 10: \[ x \leq \frac{1830}{10} \] \[ x \leq 183 \text{ pounds} \]

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

Now, we will graph this solution on a number line.

On the number line:

  • The closed point at 0 indicates that the weight cannot be below 0.
  • The closed point at 183 indicates the maximum weight per box, and everything to the right of this point represents weights greater than 183, which is not permitted.

The correct graph would show a closed point at 0, with a line extending to the right up to and including 183.

Therefore, based on the choices provided in your question, the correct depiction on a number line would be:

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.

This option correctly represents the range of feasible weights each box can have, with 183 pounds as the maximum.