This problem tests your understanding of ratios and algebraic substitution. The foundational concept is that if two ratios are equal, they can be set to a common constant, allowing you to express the variables in terms of that constant. Given the equation a/3 = b/2, we can introduce a constant, say 'k', such that a/3 = b/2 = k. This implies that a = 3k and b = 2k.
To find the value of the expression (2a + 3b)/(3a – 2b), we substitute these derived values of 'a' and 'b' into the expression:
- Numerator: 2a + 3b = 2(3k) + 3(2k) = 6k + 6k = 12k
- Denominator: 3a – 2b = 3(3k) – 2(2k) = 9k – 4k = 5k
Therefore, the expression becomes (12k)/(5k). Since 'k' is a non-zero constant, it cancels out, leaving us with 12/5. This confirms that option A is the correct answer.
The other options are incorrect because they result from miscalculations: B: 5/12 is the reciprocal of the correct answer, possibly from inverting the final fraction. C: 3/2 and D: 2/3 might arise from incorrectly simplifying the initial ratio or making errors during substitution, such as cancelling terms prematurely or incorrectly combining coefficients.