There are `12` dozen oranges in a box, `1/16` of them are rotten and `1/6` of them are to be kept for some guests. How many can be consumed?

Options

A. `112`
B. `111`
C. `113`
D. `114`

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Calculate the total number of oranges
We are given that there are `12` dozen oranges in a box. Since one dozen equals `12` oranges, we can calculate the total number of oranges as follows:

\[ \text{Total number of oranges} = 12 \times 12 = 144 \]

### Step 2: Calculate the number of rotten oranges
Next, we need to find out how many oranges are rotten. We know that `1/16` of the total oranges are rotten. Therefore, we calculate:

\[ \text{Number of rotten oranges} = \frac{1}{16} \times 144 \]

Calculating this gives:

\[ \frac{144}{16} = 9 \]

So, there are `9` rotten oranges.

### Step 3: Calculate the number of oranges kept for guests
Now, we need to determine how many oranges are kept for guests. We know that `1/6` of the total oranges are reserved for guests. Therefore, we calculate:

\[ \text{Number of oranges kept for guests} = \frac{1}{6} \times 144 \]

Calculating this gives:

\[ \frac{144}{6} = 24 \]

So, `24` oranges are kept for guests.

### Step 4: Calculate the number of oranges that can be consumed
Finally, we can find out how many oranges can be consumed by subtracting the number of rotten oranges and the number of oranges kept for guests from the total number of oranges:

\[ \text{Number of oranges that can be consumed} = \text{Total oranges} - \text{Number of rotten oranges} - \text{Number of oranges kept for guests} \]

Substituting the values we found:

\[ \text{Number of oranges that can be consumed} = 144 - 9 - 24 \]

Calculating this gives:

\[ 144 - 9 = 135 \]
\[ 135 - 24 = 111 \]

Thus, the number of oranges that can be consumed is `111`.

### Final Answer:
The number of oranges that can be consumed is **111**.

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