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George runs a manufacturing business and needs to keep track of the inventory in his warehouse each month. The table shows the change in total inventory at the end of each month last quarter.

Month Inventory Change
Jan
+
20
Feb
+
30
Mar
−
70
Which number line represents this information?

A.
The number line shows a backward arrow from 70 to 0, a backward arrow from 100 to 70, and a forward arrow from 80 to 100.

B.
The number line shows a forward arrow from 90 to 160, a backward arrow from 120 to 90, and a backward arrow from 140 to 120.

C.
The number line shows a backward arrow from 160 to 90, a forward arrow from 110 to 130, and a forward arrow from 130 to 160.

D.
The number line shows a backward arrow from 160 to 90, a forward arrow from 130 to 160, and a backward arrow from 150 to 130.

1 answer

To determine which number line accurately represents George's inventory changes, we need to analyze the given data.

Starting from an initial inventory at the beginning of January (let's assume it's 0 for simplicity):

  1. January: Inventory change is +20.

    • So, inventory at the end of January = 0 + 20 = 20.

  2. February: Inventory change is +30.

    • So, inventory at the end of February = 20 + 30 = 50.

  3. March: Inventory change is −70.

    • So, inventory at the end of March = 50 - 70 = -20 (this can represent inventory going into the negatives, which indicates that George might have run out of stock or had excess stock accounted).

Now let's summarize the final inventory balance at the end of each month:

  • End of January: 20
  • End of February: 50
  • End of March: -20

Starting from the end of January at 20, we go up to 50 at the end of February (+30) and then drop down to -20 at the end of March (-70).

Now we can analyze the proposed number line options:

A: From 70 to 0 (backward), 100 to 70 (backward), 80 to 100 (forward) - This sequence does not match our calculated inventory.

B: From 90 to 160 (forward), 120 to 90 (backward), 140 to 120 (backward) - These numbers do not correspond to the inventory values at all.

C: From 160 to 90 (backward), 110 to 130 (forward), and 130 to 160 (forward) - This also does not match our inventory changes.

D: From 160 to 90 (backward), 130 to 160 (forward), and 150 to 130 (backward) - This does not correspond to the calculated inventory.

None of the provided options directly represent the changes in George's inventory based on the calculations provided (ending at 20, 50, and -20).

If we had to put the results on a number line, it would begin at some point around 0, rise to 20 (end of January), rise to 50 (end of February), and then fall to -20 (end of March).

Unfortunately, it appears that none of the given choices accurately reflect the change in inventory based on the calculations for January, February, and March. If you have different numbers or if I'd need to reconsider or represent these changes in a different way, I'd appreciate your guidance!