If `a-3b=9b-7a`, then the ratio of a to b is

Options

A. `3:2`
B. `2:3`
C. `3:4`
D. `4:3`

Answer

To solve the equation \( a - 3b = 9b - 7a \) and find the ratio of \( a \) to \( b \), we can follow these steps:

### Step 1: Rearranging the Equation
Start with the given equation:
\[ a - 3b = 9b - 7a \]
We want to bring all terms involving \( a \) to one side and all terms involving \( b \) to the other side.

### Step 2: Move Terms
Add \( 7a \) to both sides and add \( 3b \) to both sides:
\[ a + 7a = 9b + 3b \]
This simplifies to:
\[ 8a = 12b \]

### Step 3: Finding the Ratio
Now, we need to express the ratio of \( a \) to \( b \):
\[ \frac{a}{b} = \frac{12}{8} \]
We can simplify this fraction:
\[ \frac{a}{b} = \frac{12 \div 4}{8 \div 4} = \frac{3}{2} \]

### Step 4: Conclusion
Thus, the ratio of \( a \) to \( b \) is:
\[ a : b = 3 : 2 \]