If a : b = 5 : 3, then what is the value of `(5a+3b)div(3a-2b)`?

Options

A. 34/9
B. 25/3
C. 27/5
D. 34/13

Answer

To solve the problem, we start with the given ratio \( a : b = 5 : 3 \). This means we can express \( a \) and \( b \) in terms of a common variable. Let's denote \( a = 5k \) and \( b = 3k \) for some variable \( k \).

Now, we need to find the value of the expression \( \frac{5a + 3b}{3a - 2b} \).

### Step 1: Substitute the values of \( a \) and \( b \)

Substituting \( a \) and \( b \) into the expression, we have:

\[ 5a + 3b = 5(5k) + 3(3k) = 25k + 9k = 34k \]

\[ 3a - 2b = 3(5k) - 2(3k) = 15k - 6k = 9k \]

### Step 2: Form the fraction

Now we can substitute these results back into the expression:

\[ \frac{5a + 3b}{3a - 2b} = \frac{34k}{9k} \]

### Step 3: Simplify the fraction

The \( k \) in the numerator and denominator cancels out (assuming \( k \neq 0 \)):

\[ \frac{34k}{9k} = \frac{34}{9} \]

### Step 4: Conclusion

Thus, the value of \( \frac{5a + 3b}{3a - 2b} \) is \( \frac{34}{9} \).

### Final Answer

The answer is \( \frac{34}{9} \).

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