If `5a=6b+7 and a -b =3,` what is the value of `b/2` ?

Options

A. 2
B. 4
C. `5.5`
D. 11

Explanation

To solve the given problem step by step, we will follow the equations provided and manipulate them to find the value of \( \frac{b}{2} \).

### Step 1: Write down the equations
We have two equations:
1. \( 5a = 6b + 7 \) (Equation 1)
2. \( a - b = 3 \) (Equation 2)

### Step 2: Express \( a \) in terms of \( b \)
From Equation 2, we can express \( a \) in terms of \( b \):
\[ a = b + 3 \]
Let’s call this Equation 3.

### Step 3: Substitute \( a \) in Equation 1
Now, we will substitute Equation 3 into Equation 1:
\[ 5(b + 3) = 6b + 7 \]

### Step 4: Simplify the equation
Distributing \( 5 \) on the left side:
\[ 5b + 15 = 6b + 7 \]

### Step 5: Rearrange the equation
Now, we will rearrange the equation to isolate \( b \):
\[ 5b + 15 - 7 = 6b \]
This simplifies to:
\[ 5b + 8 = 6b \]

### Step 6: Solve for \( b \)
Now, subtract \( 5b \) from both sides:
\[ 8 = 6b - 5b \]
This gives us:
\[ 8 = b \]

### Step 7: Find \( \frac{b}{2} \)
Now that we have the value of \( b \), we can find \( \frac{b}{2} \):
\[ \frac{b}{2} = \frac{8}{2} = 4 \]

### Final Answer
Thus, the value of \( \frac{b}{2} \) is \( 4 \).

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