If x is substracted from each of 19, 27, 38 and 57 the number so obtained are in per portion. Find the value of `(11x+2)`

Options

A. 54
B. 61
C. 59
D. 60

Answer

To solve the problem step by step, we need to set up the equation based on the information provided.

### Step 1: Set up the proportion
We know that if \( x \) is subtracted from each of the numbers 19, 27, 38, and 57, the resulting numbers are in proportion. This can be expressed as:
\[ \frac{19 - x}{27 - x} = \frac{38 - x}{57 - x} \]

### Step 2: Cross-multiply the proportions
To eliminate the fractions, we will cross-multiply:
\[ (19 - x)(57 - x) = (27 - x)(38 - x) \]

### Step 3: Expand both sides
Now we will expand both sides of the equation:
- Left side:
\[ 19 \cdot 57 - 19x - 57x + x^2 = 1083 - 76x + x^2 \]
- Right side:
\[ 27 \cdot 38 - 27x - 38x + x^2 = 1026 - 65x + x^2 \]

### Step 4: Set the equation
Now we can set the two expanded sides equal to each other:
\[ 1083 - 76x + x^2 = 1026 - 65x + x^2 \]

### Step 5: Simplify the equation
Since \( x^2 \) appears on both sides, we can cancel it out:
\[ 1083 - 76x = 1026 - 65x \]

### Step 6: Rearrange the equation
Now, let's rearrange the equation to isolate \( x \):
\[ 1083 - 1026 = 76x - 65x \]
\[ 57 = 11x \]

### Step 7: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{57}{11} \]

### Step 8: Find the value of \( 11x + 2 \)
Now we need to find the value of \( 11x + 2 \):
\[ 11x + 2 = 11 \left(\frac{57}{11}\right) + 2 = 57 + 2 = 59 \]

### Final Answer
Thus, the value of \( 11x + 2 \) is:
\[ \boxed{59} \]