If 57:x::51: 85, then the value of x is

Options

A. 95
B. 76
C. 114
D. none of these

Answer

To solve the problem \( 57:x::51:85 \), we can follow these steps:

### Step 1: Set up the proportion
The given ratio can be expressed as:
\[ \frac{57}{x} = \frac{51}{85} \]

### Step 2: Cross-multiply
To eliminate the fractions, we cross-multiply:
\[ 57 \times 85 = 51 \times x \]

### Step 3: Calculate \( 57 \times 85 \)
Now, we calculate \( 57 \times 85 \):
\[ 57 \times 85 = 4845 \]

### Step 4: Substitute back into the equation
Now we have:
\[ 4845 = 51 \times x \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides by 51:
\[ x = \frac{4845}{51} \]

### Step 6: Perform the division
Now we calculate \( \frac{4845}{51} \):
\[ x = 95 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{95} \]

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