IF `b+22/25=7/5 b`, what is the value of b?

Answer

To solve the equation \( b + \frac{22}{25} = \frac{7}{5}b \), we will follow these steps:

### Step 1: Write down the equation
The given equation is:
\[ b + \frac{22}{25} = \frac{7}{5}b \]

### Step 2: Subtract \( b \) from both sides
To isolate the terms involving \( b \), we subtract \( b \) from both sides:
\[ \frac{22}{25} = \frac{7}{5}b - b \]

### Step 3: Simplify the right side
The right side can be simplified. We can express \( b \) as \( \frac{5b}{5} \) to have a common denominator:
\[ \frac{22}{25} = \frac{7b - 5b}{5} = \frac{2b}{5} \]

### Step 4: Eliminate the fraction
To eliminate the fraction, we multiply both sides by 5:
\[ 5 \cdot \frac{22}{25} = 2b \]
This simplifies to:
\[ \frac{110}{25} = 2b \]

### Step 5: Simplify the left side
Now, simplify \( \frac{110}{25} \):
\[ \frac{110}{25} = \frac{22}{5} \]
So we have:
\[ \frac{22}{5} = 2b \]

### Step 6: Solve for \( b \)
Now, divide both sides by 2:
\[ b = \frac{22}{5} \div 2 = \frac{22}{10} \]
This simplifies to:
\[ b = \frac{11}{5} \]

### Final Answer
Thus, the value of \( b \) is:
\[ b = \frac{11}{5} \]