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 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 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 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.

Answer 1

To determine how much each box of books can weigh without exceeding the maximum weight of the elevator (2000 pounds), we need to follow these steps:

1. Calculate the total weight capacity available for the boxes:

   • Maximum weight of the elevator = 2000 pounds
   • Weight of Lionel = 170 pounds
   • Weight capacity for boxes = Maximum weight of elevator - Weight of Lionel
   • Weight capacity for boxes = 2000 - 170 = 1830 pounds

2. Determine the maximum weight per box:

   • Since there are 10 boxes of books, we divide the total weight capacity for the boxes by the number of boxes:
   • Maximum weight per box = Weight capacity for boxes / Number of boxes
   • Maximum weight per box = 1830 pounds / 10 boxes = 183 pounds

Thus, each box can weigh at most 183 pounds.

3. Graph the solution on a number line:
   • The number line should show the range of possible weights for each box from 0 to greater than or equal to 183 pounds.
   • A closed point should be plotted at 183, indicating that this is the maximum weight each box can weigh without exceeding the elevator's capacity.
   • A line should extend to the right, indicating that the weight of the boxes can be 183 pounds or less.

Considering the above calculation and analysis, the correct graph response among the options provided is the one that shows a closed point at 183 with a line extending to the right. The option denoting this should be selected.