An all-natural health clinic stocks teas and herbs in a 5:11 ratio at one of its warehouse. In an effort to cut overhead costs, the owners close this warehouse and tranfer its stock to a larger warehouse, increasing that warehouses inventory of items by 20%. Which of the following could be the number of items at the larger warehouse after the transfer?

Options

A. `198`
B. `386`
C. `480`
D. `573`

Explanation

To solve the problem step by step, we will follow the logic laid out in the video transcript.

### Step 1: Understand the Ratio
The ratio of teas to herbs in the small warehouse is given as 5:11. This means for every 5 units of tea, there are 11 units of herbs.

### Step 2: Define Variables
Let’s assume the number of teas is \( 5x \) and the number of herbs is \( 11x \), where \( x \) is a common multiplier.

### Step 3: Calculate Total Stock in Small Warehouse
The total stock in the small warehouse can be calculated as:
\[ \text{Total stock} = \text{Number of teas} + \text{Number of herbs} = 5x + 11x = 16x \]

### Step 4: Understand the Increase in Inventory
It is given that when the stock from the small warehouse is transferred to the larger warehouse, the total inventory in the larger warehouse increases by 20%. This means the total stock in the larger warehouse after the transfer can be expressed as:
\[ \text{New total stock} = \text{Original stock in larger warehouse} + \text{Stock from small warehouse} \]

### Step 5: Set Up the Equation
Let’s denote the original stock in the larger warehouse as \( W \). The increase of 20% means:
\[ \text{New total stock} = W + 16x = 1.2W \]

### Step 6: Rearranging the Equation
Rearranging the equation gives us:
\[ W + 16x = 1.2W \]
\[ 16x = 1.2W - W \]
\[ 16x = 0.2W \]
\[ W = \frac{16x}{0.2} = 80x \]

### Step 7: Calculate Total Stock in Larger Warehouse After Transfer
Now, we can find the total stock in the larger warehouse after the transfer:
\[ \text{Total stock after transfer} = W + 16x = 80x + 16x = 96x \]

### Step 8: Determine Possible Values
Since \( 96x \) must be a multiple of 96, we need to find the possible values for \( 96x \).

### Conclusion
The total number of items in the larger warehouse after the transfer must be a multiple of 96.