1. **State the problem:** Solve the system of equations: $$\frac{9}{2}x + 4y = 27$$ $$\frac{3}{2}x + 4y = 21$$ Find the value of $$\frac{17}{2}x + 6y$$. 2. **Use elimination or substitution:** Subtract the second equation from the first to eliminate $$y$$: $$\left(\frac{9}{2}x + 4y\right) - \left(\frac{3}{2}x + 4y\right) = 27 - 21$$ $$\frac{9}{2}x - \frac{3}{2}x = 6$$ $$\frac{6}{2}x = 6$$ $$3x = 6$$ $$x = 2$$ 3. **Substitute $$x=2$$ into one of the original equations to find $$y$$:** Using $$\frac{3}{2}x + 4y = 21$$: $$\frac{3}{2} \times 2 + 4y = 21$$ $$3 + 4y = 21$$ $$4y = 18$$ $$y = \frac{18}{4} = \frac{9}{2} = 4.5$$ 4. **Calculate $$\frac{17}{2}x + 6y$$:** $$\frac{17}{2} \times 2 + 6 \times \frac{9}{2} = 17 + 27 = 44$$ 5. **Answer:** The value is 44, which corresponds to option C.