1. **State the problem:** The florist assembles small and large flower arrangements. We want to find the time it takes to assemble each type. 2. **Define variables:** Let $x$ = time in minutes to assemble one small arrangement. Let $y$ = time in minutes to assemble one large arrangement. 3. **Write the system of equations based on the problem:** From the morning work: $$12x + 6y = 114$$ From the afternoon work: $$12x + 1y = 69$$ 4. **Use elimination to solve the system:** Subtract the second equation from the first to eliminate $x$: $$\cancel{12x} + 6y = 114$$ $$- (\cancel{12x} + 1y = 69)$$ ------------------------- $$5y = 45$$ 5. **Solve for $y$:** $$y = \frac{45}{5} = 9$$ 6. **Substitute $y=9$ into the second equation to find $x$:** $$12x + 1(9) = 69$$ $$12x + 9 = 69$$ $$12x = 69 - 9 = 60$$ $$x = \frac{60}{12} = 5$$ 7. **Answer:** The florist can assemble a small arrangement in **5** minutes and a large one in **9** minutes.