`a + b + c//2 = 60`
`-a - b + c//2 = -10`
`{:("Column A" , " ","ColumnB"),(b, ,c):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the given equations and compare the values in Column A (B) and Column B (C), we will follow these steps:

### Step 1: Write down the equations
We are given two equations:
1. \( a + b + \frac{c}{2} = 60 \)
2. \( -a - b + \frac{c}{2} = -10 \)

### Step 2: Add the two equations
To eliminate \(a\) and \(b\), we can add the two equations together:
\[ (a + b + \frac{c}{2}) + (-a - b + \frac{c}{2}) = 60 + (-10) \]
This simplifies to:
\[ \frac{c}{2} + \frac{c}{2} = 50 \]
\[ c = 50 \]

### Step 3: Substitute the value of \(c\) back into one of the equations
Now that we have \(c\), we can substitute it back into the first equation:
\[ a + b + \frac{50}{2} = 60 \]
This simplifies to:
\[ a + b + 25 = 60 \]
\[ a + b = 60 - 25 \]
\[ a + b = 35 \]

### Step 4: Analyze the results
From our calculations, we have:
- \(c = 50\)
- \(a + b = 35\)

### Step 5: Compare the columns
Now we need to compare Column A (which is \(b\)) and Column B (which is \(c\)):
- We know \(c = 50\), but we do not have individual values for \(a\) and \(b\). We only know that \(a + b = 35\).

Since \(b\) can take any value such that \(a + b = 35\), we cannot definitively say whether \(b\) is greater than, less than, or equal to \(c\) (50).

### Conclusion
Since we do not have enough information to determine the relationship between \(b\) and \(c\), the correct answer is that there is not enough information to decide.

### Final Answer
**Option 4: If there is not enough information to decide.**

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