To determine how much each box can weigh, we first need to account for Lionel's weight and the maximum weight capacity of the elevator.
- The maximum weight of the elevator is 2,000 pounds.
- Lionel weighs 170 pounds.
To find the total weight that can be allocated to the boxes, we subtract Lionel's weight from the elevator's total capacity:
\[ \text{Weight available for boxes} = \text{Maximum weight} - \text{Lionel's weight} \] \[ \text{Weight available for boxes} = 2000 \text{ lbs} - 170 \text{ lbs} = 1830 \text{ lbs} \]
Next, we have 10 boxes of books, and we denote the weight of each box as \( x \). Therefore, the total weight of the 10 boxes can be expressed as \( 10x \).
We need to ensure that the total weight of the boxes does not exceed the available weight:
\[ 10x \leq 1830 \]
Next, we can solve for \( x \):
\[ x \leq \frac{1830}{10} \] \[ x \leq 183 \]
Thus, each box can weigh a maximum of 183 pounds.
Graphing the Solution on a Number Line
The solution can be represented on a number line ranging from 0 to 200. A closed point is plotted at 0, and an arrow is drawn from 0 to 183, where the closed point at 183 indicates that this weight is included in the solution (meaning \( x \) can equal 183 but not exceed it).
The final setup would look like this:
- Closed point at 0.
- A line extends from that point to the right, connecting with a closed point at 183.
This indicates that the weight of each box can be anywhere from 0 pounds up to and including 183 pounds.
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