if `3a-c=5b and 3a+3b-c=40`, what is the value of b?

Answer

To solve the equations \(3a - c = 5b\) and \(3a + 3b - c = 40\) for the value of \(b\), we can follow these steps:

### Step 1: Rearranging the first equation
The first equation is:
\[ 3a - c = 5b \]
We can rearrange this equation to isolate \(c\):
\[ c = 3a - 5b \]
Let's label this as Equation 1.

### Step 2: Substitute \(c\) in the second equation
Now, we take the second equation:
\[ 3a + 3b - c = 40 \]
We will substitute the expression for \(c\) from Equation 1 into this equation:
\[ 3a + 3b - (3a - 5b) = 40 \]

### Step 3: Simplifying the equation
Now, simplify the left-hand side:
\[ 3a + 3b - 3a + 5b = 40 \]
This simplifies to:
\[ 3b + 5b = 40 \]
Combining like terms gives:
\[ 8b = 40 \]

### Step 4: Solve for \(b\)
Now, divide both sides by 8 to solve for \(b\):
\[ b = \frac{40}{8} = 5 \]

### Final Answer
Thus, the value of \(b\) is:
\[ \boxed{5} \]