The average of three numbers of which greatest is 16 is 12. If the smallest is half of the greatest, the remaining number is:

Options

A. 12
B. 8
C. 14
D. 10

Answer

To solve the problem step by step, let's denote the three numbers as A, B, and C. We know the following:

1. The greatest number (A) is 16.
2. The average of the three numbers is 12.
3. The smallest number (C) is half of the greatest number (A).

### Step 1: Write down the average formula
The average of three numbers A, B, and C can be expressed as:
\[ \text{Average} = \frac{A + B + C}{3} \]
Given that the average is 12, we can set up the equation:
\[ \frac{A + B + C}{3} = 12 \]

### Step 2: Multiply both sides by 3
To eliminate the fraction, multiply both sides by 3:
\[ A + B + C = 12 \times 3 \]
\[ A + B + C = 36 \]

### Step 3: Substitute the value of A
We know that A (the greatest number) is 16, so we substitute A into the equation:
\[ 16 + B + C = 36 \]

### Step 4: Rearrange the equation
Now, we can rearrange this equation to find B + C:
\[ B + C = 36 - 16 \]
\[ B + C = 20 \]

### Step 5: Find the value of C
We are also given that the smallest number (C) is half of the greatest number (A). Therefore:
\[ C = \frac{A}{2} = \frac{16}{2} = 8 \]

### Step 6: Substitute the value of C into the equation
Now we can substitute the value of C back into the equation we derived for B + C:
\[ B + 8 = 20 \]

### Step 7: Solve for B
Now, we can solve for B:
\[ B = 20 - 8 \]
\[ B = 12 \]

### Final Answer
The remaining number (B) is **12**.

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