1. **State the problem:** Kialani sells orchids and lilies at different prices. We know: - 8 orchids + 12 lilies = 362 - 12 orchids + 8 lilies = 388 We want to find the price of one lily plant. 2. **Define variables:** Let $x$ be the price of one orchid. Let $y$ be the price of one lily. 3. **Translate to equations:** From the problem: $$8x + 12y = 362$$ $$12x + 8y = 388$$ 4. **Solve the system of equations:** Multiply the first equation by 3 and the second by 2 to align coefficients for elimination of $x$: $$24x + 36y = 1086$$ $$24x + 16y = 776$$ Subtract the second from the first: $$(24x + 36y) - (24x + 16y) = 1086 - 776$$ $$20y = 310$$ Divide both sides by 20: $$y = \frac{310}{20} = 15.5$$ 5. **Interpret the result:** The price of one lily plant $y$ is $15.5$. 6. **Verify by finding $x$:** Use the first equation: $$8x + 12(15.5) = 362$$ $$8x + 186 = 362$$ $$8x = 362 - 186 = 176$$ $$x = \frac{176}{8} = 22$$ Everything checks out. **Final answer:** The lily plant costs $15.5$.