A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6. getting 112 as the answer. The correct answer should have been

Options

A. 124
B. 122
C. 118
D. 114

Answer

To solve the problem step by step, we will begin by defining the unknown number and then setting up the equations based on the student's actions.

### Step 1: Define the unknown number
Let the unknown number be \( x \).

### Step 2: Set up the equation based on the student's incorrect method
The student first added 12 to the number and then divided the result by 6. According to the problem, this resulted in an answer of 112. Therefore, we can set up the equation:
\[ \frac{x + 12}{6} = 112 \]

### Step 3: Solve for \( x \)
To eliminate the fraction, we multiply both sides of the equation by 6:
\[ x + 12 = 112 \times 6 \]
Calculating the right side:
\[ x + 12 = 672 \]
Next, we isolate \( x \) by subtracting 12 from both sides:
\[ x = 672 - 12 \]
\[ x = 660 \]

### Step 4: Calculate the correct answer
Now that we have found the value of \( x \), we need to find the correct answer according to the original instructions, which were to divide \( x \) by 6 and then add 12:
\[ \text{Correct Answer} = \left(\frac{x}{6}\right) + 12 \]
Substituting \( x = 660 \):
\[ \text{Correct Answer} = \left(\frac{660}{6}\right) + 12 \]
Calculating \( \frac{660}{6} \):
\[ \frac{660}{6} = 110 \]
Now adding 12:
\[ \text{Correct Answer} = 110 + 12 = 122 \]

### Final Answer
The correct answer should have been \( 122 \).

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