If `a` is greater than b by 2 and b is greater than c by 10 and a+b+c = 130 , then value of (b+c) -a is

Options

A. 28
B. 32
C. 34
D. 44

Explanation

To solve the problem step by step, we will use the information given in the question.

### Step 1: Set up the equations based on the given conditions.
1. We know that \( a \) is greater than \( b \) by 2. This can be written as:
\[ a = b + 2 \]
2. We also know that \( b \) is greater than \( c \) by 10. This can be expressed as:
\[ b = c + 10 \]
3. The total of \( a + b + c \) is given to be 130:
\[ a + b + c = 130 \]

### Step 2: Substitute the expressions for \( a \) and \( c \) into the total equation.
From the first equation, substitute \( a \) into the total equation:
\[ (b + 2) + b + c = 130 \]
Now substitute \( c \) from the second equation \( c = b - 10 \) into the equation:
\[ (b + 2) + b + (b - 10) = 130 \]

### Step 3: Simplify the equation.
Combine like terms:
\[ b + 2 + b + b - 10 = 130 \]
This simplifies to:
\[ 3b - 8 = 130 \]

### Step 4: Solve for \( b \).
Add 8 to both sides:
\[ 3b = 138 \]
Now divide by 3:
\[ b = 46 \]

### Step 5: Find the values of \( a \) and \( c \).
Using the value of \( b \):
1. Substitute \( b \) back into the equation for \( a \):
\[ a = b + 2 = 46 + 2 = 48 \]
2. Substitute \( b \) back into the equation for \( c \):
\[ c = b - 10 = 46 - 10 = 36 \]

### Step 6: Calculate \( (b + c) - a \).
Now we can find \( (b + c) - a \):
\[ (b + c) - a = (46 + 36) - 48 \]
Calculate \( b + c \):
\[ b + c = 82 \]
Now subtract \( a \):
\[ 82 - 48 = 34 \]

### Final Answer:
The value of \( (b + c) - a \) is \( 34 \).