1. **State the problem:** We have a fruit bowl with oranges, kiwis, and limes. The ratio of oranges to kiwis is 3:5. The probability of picking an orange is $\frac{1}{4}$. We need to find the probability of picking a lime. 2. **Set up variables:** Let the number of oranges be $3x$ and the number of kiwis be $5x$ based on the ratio. Let the number of limes be $y$. 3. **Total fruits:** Total fruits = oranges + kiwis + limes = $3x + 5x + y = 8x + y$. 4. **Probability of orange:** Given as $\frac{1}{4}$, so $$\frac{3x}{8x + y} = \frac{1}{4}$$ 5. **Solve for $y$:** Cross-multiply: $$4 \times 3x = 1 \times (8x + y)$$ $$12x = 8x + y$$ Subtract $8x$ from both sides: $$12x - 8x = y$$ $$4x = y$$ 6. **Find probability of lime:** Probability of lime = number of limes / total fruits = $$\frac{y}{8x + y} = \frac{4x}{8x + 4x} = \frac{4x}{12x} = \frac{4}{12} = \frac{1}{3}$$ **Final answer:** The probability that the fruit picked is a lime is $\frac{1}{3}$.