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.
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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: \[ 2000 - 170 = 1830 \text{ pounds} \]
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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.
- 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.