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 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.
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, we first need to account for Lionel's weight as he operates the elevator.

1. Identify the maximum weight capacity of the elevator: 2000 pounds.
2. Identify Lionel's weight: 170 pounds.

Next, we'll subtract Lionel's weight from the total weight that the elevator can hold:

\[ \text{Maximum weight for boxes} = \text{Maximum elevator weight} - \text{Lionel's weight} \]

\[ \text{Maximum weight for boxes} = 2000 \text{ pounds} - 170 \text{ pounds} = 1830 \text{ pounds} \]

Now, since Lionel has 10 boxes of books, we can determine the maximum weight allowed for each box by dividing the total weight for the boxes by the number of boxes:

\[ \text{Weight per box} = \frac{\text{Maximum weight for boxes}}{\text{Number of boxes}} = \frac{1830 \text{ pounds}}{10} = 183 \text{ pounds} \]

This means that each box can weigh at most 183 pounds.

Graphing the Solution:

On a number line, we are interested in the possible range of weights for each box. Since each box can weigh anywhere from 0 to 183 pounds, we would represent this on our number line.

• A closed point would be plotted at 0 (the minimum weight) and a closed point plotted at 183 (the maximum weight).
• The line would connect these two points to indicate all possible weights each box could have.

Therefore, the correct illustration 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 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 183.

This visual representation shows that each box can weigh from 0 pounds up to 183 pounds, inclusive.