A military supply depot transfers 40\% of its medical kit inventory to a forward operating… — Armed Services Vocational Aptitude Battery (ASVAB)

A military supply depot transfers $40\%$ of its medical kit inventory to a forward operating base. The following week, the depot transfers $30\%$ of its remaining medical kits to a local training facility. If the depot currently has $1,260$ medical kits left in stock, what was the original number of medical kits in the inventory?

$3,000$ Answer
B
$4,200$
C
$7,000$
D
$2,142$

Answer

The original number of medical kits in the inventory was

3,000

The correct approach requires tracking the percentages relative to the original inventory. After

40\%

of the kits are transferred,

60\%

remains. The second transfer removes

30\%

of this

60\%

, meaning

70\%

of the

60\%

stays in stock. Multiplying

0.60 \times 0.70

gives

0.42

, which means the final

1,260

kits represent exactly

42\%

of the original inventory. Dividing

1,260

0.42

yields the original starting total of

3,000

Step-by-Step Solution

Determine the percentage of inventory remaining after the first transfer.

100\% - 40\% = 60\%

of the original inventory remains.

The second transfer is based on this remaining amount, not the original total.

Calculate the percentage of the original inventory that remains after the second transfer.

The second transfer takes

30\%

of the remaining kits, meaning

70\%

of those kits stay at the depot.

0.70 \times 0.60 = 0.42

, so

42\%

of the original inventory is left.

To set up an equation, the final quantity must be related to a single percentage representing a portion of the original whole.

Solve for the original number of medical kits.

Let

x

be the original inventory.

0.42x = 1,260

. Dividing both sides by

0.42

gives

x = 1,260 \div 0.42 = 3,000

Dividing the final remaining quantity by its corresponding decimal percentage yields the original starting value.

Key Concept

Calculating successive percentages and working backward from a final quantity to find an original whole.

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