11x+12y=58 and 12x+11y=57, the value of 4(x+y) is

Options

A. 5
B. 12
C. 20
D. 24

Answer

To solve the equations \(11x + 12y = 58\) and \(12x + 11y = 57\) and find the value of \(4(x+y)\), follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \(11x + 12y = 58\) (Equation 1)
2. \(12x + 11y = 57\) (Equation 2)

### Step 2: Add the two equations
We will add Equation 1 and Equation 2:
\[ (11x + 12y) + (12x + 11y) = 58 + 57 \]
This simplifies to:
\[ 23x + 23y = 115 \]

### Step 3: Factor out the common term
We can factor out 23 from the left side:
\[ 23(x + y) = 115 \]

### Step 4: Solve for \(x + y\)
Now, divide both sides by 23:
\[ x + y = \frac{115}{23} \]
Calculating the right side gives:
\[ x + y = 5 \]

### Step 5: Calculate \(4(x + y)\)
Now we need to find \(4(x + y)\):
\[ 4(x + y) = 4 \times 5 = 20 \]

### Final Answer
Thus, the value of \(4(x + y)\) is \(20\).

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