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 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.

Answer 1

To find out how much each box of books can weigh without exceeding the elevator's maximum weight limit, we first need to consider Lionel's weight and the total weight limit of the elevator.

1. Calculate Total Weight Limit:

   • Maximum weight of the elevator = 2000 pounds
   • Weight of Lionel = 170 pounds
   • Therefore, the maximum weight allowed for the boxes is: \[ 2000 - 170 = 1830 \text{ pounds} \]

2. Determine Weight Per Box:

   • There are 10 boxes of books.
   • Let \( x \) be the weight of each box. The total weight of the boxes can be expressed as \( 10x \).
   • The inequality for the total weight of the boxes needs to satisfy: \[ 10x \leq 1830 \]
   • To find \( x \), divide both sides by 10: \[ x \leq \frac{1830}{10} = 183 \]

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

3. Graphing the Solution:
   • On the number line, we plot the closed point at 183 (indicating that 183 pounds is included in the solution since it can weigh up to that amount).
   • We then draw a line extending to the right from 183, indicating that any weight greater than 183 pounds is not allowed.

Thus, the representation on the number line would show that each box can weigh up to 183 pounds, and it is graphically represented with a closed point at 183 and a line extending to the right.

So, the correct representation from the options provided would be: An illustration showing a closed point at 183 with a line extending from that point to the right.