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 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 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 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.

Answer 1

To determine how much each box can weigh, we can denote the weight of each box as \( x \).

1. Identify the maximum weight allowed in the elevator:

   • The maximum weight allowed in the elevator is 2,000 pounds.

2. Account for Lionel's weight:

   • Lionel weighs 170 pounds. Therefore, the weight limit for the boxes themselves is: \[ 2000 \text{ pounds} - 170 \text{ pounds} = 1830 \text{ pounds} \]

3. Calculate the weight for each box:

   • There are 10 boxes, so the total weight of the boxes can be represented as \( 10x \). To not exceed the remaining weight limit, we set up the following inequality: \[ 10x \leq 1830 \]

4. Solve for \( x \): \[ x \leq \frac{1830}{10} \] \[ x \leq 183 \]

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

Graphing the Solution:

On a number line labeled "Weight of Each Box in the Elevator," you would plot:

• Closed point at 0 (representing that the weight can't be negative).
• A line extending from 0 to a closed point at 183 (since each box of books can weigh anywhere from 0 to 183 pounds).

The correct depiction on the number line given the options would thus be shown in the option with the range from 0 to 200 and closed points at 0 and 183.

Therefore, the answer is:

• 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.