47 is added to the product of 71 and an unknown number. The new number is divisible by 7 giving the quotient 98. The unknown number is a multiple of

Options

A. 2
B. 5
C. 7
D. 3

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the problem
We are given that 47 is added to the product of 71 and an unknown number \( x \). The resulting number is divisible by 7, and the quotient when this number is divided by 7 is 98.

### Step 2: Set up the equation
From the information given, we can set up the equation:
\[ 71x + 47 = 7 \times 98 \]

### Step 3: Calculate the right side of the equation
Now, calculate \( 7 \times 98 \):
\[ 7 \times 98 = 686 \]
So, we can rewrite our equation as:
\[ 71x + 47 = 686 \]

### Step 4: Isolate the unknown number \( x \)
Next, we need to isolate \( x \). We can do this by subtracting 47 from both sides:
\[ 71x = 686 - 47 \]
Calculating the right side:
\[ 686 - 47 = 639 \]
So, we have:
\[ 71x = 639 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 71 to find \( x \):
\[ x = \frac{639}{71} \]
Calculating the division:
\[ x = 9 \]

### Step 6: Determine if \( x \) is a multiple of the given options
The problem states that the unknown number \( x \) is a multiple of something. Since we found \( x = 9 \), we can check if it is a multiple of the options provided (if any were given).

### Conclusion
Thus, the unknown number \( x \) is 9.

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