If `a+2b = 55` and `a - 2b = -13` , find the value of b .
A. 21
B. 14
C. 17
D. 19

Options

A. D
B. A
C. C
D. B

Answer

To solve the equations \( a + 2b = 55 \) and \( a - 2b = -13 \) for the value of \( b \), we can follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \( a + 2b = 55 \) (Equation 1)
2. \( a - 2b = -13 \) (Equation 2)

### Step 2: Subtract Equation 2 from Equation 1
We can eliminate \( a \) by subtracting Equation 2 from Equation 1:
\[ (a + 2b) - (a - 2b) = 55 - (-13) \]
This simplifies to:
\[ a + 2b - a + 2b = 55 + 13 \]
\[ 4b = 68 \]

### Step 3: Solve for \( b \)
Now, we can solve for \( b \) by dividing both sides by 4:
\[ b = \frac{68}{4} = 17 \]

### Conclusion
The value of \( b \) is \( 17 \).

### Final Answer
Thus, the correct option is **C. 17**.

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