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)

Question

Responses

1.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.

2.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.

3.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.

4.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 find how much each box of books can weigh without exceeding the maximum weight of the elevator, we start by determining the total weight capacity.

1. The maximum weight capacity of the elevator is 2000 pounds.
2. Lionel's weight is 170 pounds.
3. The total weight of the boxes and Lionel combined should not exceed 2000 pounds.

Let's denote the weight of each box of books as \( x \). Since there are 10 boxes, the total weight of the boxes is \( 10x \).

We set up an inequality:

\[ 10x + 170 \leq 2000 \]

Next, we isolate \( x \):

\[ 10x \leq 2000 - 170 \] \[ 10x \leq 1830 \] \[ x \leq \frac{1830}{10} \] \[ x \leq 183 \]

This means each box of books can weigh up to a maximum of 183 pounds.

Now, we represent this solution on a number line. The range of potential weights for each box is from 0 to 183 (inclusive).

Therefore, the correct response is:

Option 2: 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.