1. **State the problem:** Find the value of the expression $$\frac{3m + 2n}{3k - 2m}$$ when $$m=4$$, $$n=3$$, and $$k=5$$. 2. **Write the expression with given values:** Substitute $$m=4$$, $$n=3$$, and $$k=5$$ into the expression: $$\frac{3(4) + 2(3)}{3(5) - 2(4)}$$ 3. **Calculate numerator:** $$3(4) + 2(3) = 12 + 6 = 18$$ 4. **Calculate denominator:** $$3(5) - 2(4) = 15 - 8 = 7$$ 5. **Form the fraction:** $$\frac{18}{7}$$ 6. **Simplify if possible:** 18 and 7 have no common factors other than 1, so the fraction is already in simplest form. 7. **Final answer:** $$\frac{18}{7}$$ or approximately 2.5714.