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 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.

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.
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with one I can only chose 1

Answer 1

To solve the problem of how much each box of books can weigh, we can set up the equation based on the maximum weight capacity of the elevator:

1. The maximum allowed weight in the elevator is 2,000 pounds.
2. Lionel's weight is 170 pounds.
3. Let \( x \) represent the weight of each box of books.
4. There are 10 boxes of books.

The total weight in the elevator can be represented as: \[ \text{Total weight} = \text{weight of Lionel} + \text{weight of boxes} = 170 + 10x \] We need to ensure that this total weight does not exceed the maximum capacity: \[ 170 + 10x \leq 2000 \]

Now, we can solve for \( x \):

1. Subtract 170 from both sides: \[ 10x \leq 2000 - 170 \] \[ 10x \leq 1830 \]

2. Divide by 10: \[ x \leq 183 \]

This means that each box can weigh a maximum of 183 pounds.

Now, based on this calculation, we will choose the appropriate graph to represent the solution on the number line.

We need to find the correct option that represents this finding:

• The number line must show a closed point at 183, with shading extending to the right (indicating that each box can weigh 183 pounds or less).

So, the correct representation 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.

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