If (a+b+c)/(3)=(a+b)/(2)`, then c=

Options

A. `(a-b)/(2)`
B. `(a+b)/(2)`
C. `5a+5b`
D. `(a+b)/(5)`

Answer

To solve the equation \(\frac{a+b+c}{3} = \frac{a+b}{2}\) for \(c\), we will follow these steps:

### Step 1: Eliminate the fractions
Multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 6.

\[ 6 \cdot \left(\frac{a+b+c}{3}\right) = 6 \cdot \left(\frac{a+b}{2}\right) \]

### Step 2: Simplify the equation
This gives us:

\[ 2(a+b+c) = 3(a+b) \]

### Step 3: Distribute the terms
Now, distribute on both sides:

\[ 2a + 2b + 2c = 3a + 3b \]

### Step 4: Rearrange the equation
Next, we want to isolate \(c\). Subtract \(2a\) and \(2b\) from both sides:

\[ 2c = 3a + 3b - 2a - 2b \]

### Step 5: Combine like terms
This simplifies to:

\[ 2c = (3a - 2a) + (3b - 2b) \]
\[ 2c = a + b \]

### Step 6: Solve for \(c\)
Finally, divide both sides by 2 to solve for \(c\):

\[ c = \frac{a + b}{2} \]

### Final Answer:
Thus, the value of \(c\) is:

\[ c = \frac{a + b}{2} \]

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