If a/b=4/3, then what is the value of `(3a+2b)div(a-b)`?

Options

A. 6
B. 12
C. 18
D. 24

Answer

To solve the problem, we start with the given ratio and manipulate it to find the desired expression. Let's break it down step by step.

### Step-by-Step Solution:

1. **Given Information**:
We know that \( \frac{a}{b} = \frac{4}{3} \).

2. **Express \( a \) in terms of \( b \)**:
From the ratio, we can express \( a \) as:
\[ a = \frac{4}{3}b \]

3. **Substitute \( a \) into the expression**:
We need to find the value of \( \frac{3a + 2b}{a - b} \). Substituting \( a \) from step 2 into the expression gives:
\[ \frac{3\left(\frac{4}{3}b\right) + 2b}{\frac{4}{3}b - b} \]

4. **Simplify the numerator**:
The numerator becomes:
\[ 3\left(\frac{4}{3}b\right) + 2b = 4b + 2b = 6b \]

5. **Simplify the denominator**:
The denominator becomes:
\[ \frac{4}{3}b - b = \frac{4}{3}b - \frac{3}{3}b = \frac{1}{3}b \]

6. **Combine the results**:
Now we can substitute the simplified numerator and denominator back into the expression:
\[ \frac{6b}{\frac{1}{3}b} \]

7. **Simplify the fraction**:
Dividing \( 6b \) by \( \frac{1}{3}b \) gives:
\[ 6b \div \frac{1}{3}b = 6b \times \frac{3}{1} = 18 \]

### Final Answer:
Thus, the value of \( \frac{3a + 2b}{a - b} \) is \( 18 \).