To determine which number line correctly represents the inventory changes that George experienced from January to March, we can start by calculating the total inventory change over those months.
- Starting Inventory in January: Let's assume it is 100 (for simplicity).
- January Change: +20
- New Inventory = 100 + 20 = 120
- February Change: +30
- New Inventory = 120 + 30 = 150
- March Change: -70
- New Inventory = 150 - 70 = 80
After this sequence of changes, George's inventory at the end of March is 80.
Now, let's outline the changes:
- Start at 100 in January.
- The inventory increases to 120 (January change).
- The inventory then increases to 150 (February change).
- Finally, it decreases to 80 (March change).
Now, let's analyze each option to see which one represents these changes:
Option A:
- Moves backward from 70 to 0, then backward from 100 to 70, and then forward from 80 to 100. The movements do not match our findings.
Option B:
- Moves forward from 90 to 160 (no match, should be 100 to 150), then backward from 120 to 90 (inconsistent), and backward again from 140 to 120 (inconsistent).
Option C:
- Moves backward from 160 to 90 (no match), forward from 110 to 130 (inconsistent), and forward from 130 to 160 (inconsistent).
Option D:
- Moves backward from 160 to 90 (no match), forward from 130 to 160 (inconsistent), and backward from 150 to 130 (inconsistent).
None of the provided options correctly represents the changes in inventory from January to March based on the calculations.
If we reconsider the inventory as a cumulative change rather than specific start numbers, we note:
- Start from an unspecified point (assumed 100).
- Incrementally upward movements and a final downward movement can only be represented if the intermediate values are accurately plotted.
Since none of the options directly correlate and provide a clear visual of the increase followed by a decrease as per the calculations provided, I conclude that none of the options represent this information correctly.
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