If ` ( 3a+ 5b)/(3a- 5b) = 5`, then a: b is equal to

Options

A. ` 2: 1`
B. ` 5 : 3`
C. ` 3 : 2`
D. ` 5 : 2`

Answer

To solve the equation \( \frac{3a + 5b}{3a - 5b} = 5 \) and find the ratio \( a:b \), we can follow these steps:

### Step 1: Set up the equation
We start with the given equation:
\[ \frac{3a + 5b}{3a - 5b} = 5 \]

### Step 2: Cross-multiply
To eliminate the fraction, we cross-multiply:
\[ 3a + 5b = 5(3a - 5b) \]

### Step 3: Distribute on the right side
Now, distribute the 5 on the right side:
\[ 3a + 5b = 15a - 25b \]

### Step 4: Rearrange the equation
Next, we rearrange the equation to group like terms:
\[ 3a + 5b - 15a + 25b = 0 \]
This simplifies to:
\[ -12a + 30b = 0 \]

### Step 5: Solve for the ratio
Now, we can isolate \( a \) and \( b \):
\[ 12a = 30b \]
Dividing both sides by 6 gives:
\[ 2a = 5b \]
Now, dividing both sides by \( b \) (assuming \( b \neq 0 \)):
\[ \frac{a}{b} = \frac{5}{2} \]

### Step 6: Write the ratio
Thus, the ratio \( a:b \) can be expressed as:
\[ a:b = 5:2 \]

### Final Answer
The ratio \( a:b \) is \( 5:2 \).

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