`2/11` of x is equal to y and the respective ratio between `(x+16)` and y is 37:6. What is the value of x?

Options

A. 121
B. 132
C. 110
D. 108

Answer

To solve the problem step by step, we need to follow the given conditions carefully.

### Step 1: Express y in terms of x
The first condition given is:
\[ \frac{2}{11} \cdot x = y \]
This means that:
\[ y = \frac{2}{11} x \]

### Step 2: Set up the ratio
The second condition states that the ratio between \( (x + 16) \) and \( y \) is \( 37:6 \). We can express this as:
\[ \frac{x + 16}{y} = \frac{37}{6} \]
Cross-multiplying gives:
\[ 6(x + 16) = 37y \]

### Step 3: Substitute y
Now, substitute \( y \) from Step 1 into the equation from Step 2:
\[ 6(x + 16) = 37\left(\frac{2}{11} x\right) \]
This simplifies to:
\[ 6(x + 16) = \frac{74}{11} x \]

### Step 4: Clear the fraction
To eliminate the fraction, multiply both sides by 11:
\[ 11 \cdot 6(x + 16) = 74x \]
This simplifies to:
\[ 66(x + 16) = 74x \]

### Step 5: Expand and rearrange
Expanding the left side gives:
\[ 66x + 1056 = 74x \]
Now, rearranging the equation to isolate \( x \):
\[ 1056 = 74x - 66x \]
\[ 1056 = 8x \]

### Step 6: Solve for x
Now, divide both sides by 8:
\[ x = \frac{1056}{8} = 132 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{132} \]