1. **State the problem:** Jake wants to make cupcakes using a recipe for 8 cupcakes that requires 30g caster sugar and 50g butter per 8 cupcakes. He has unlimited flour, milk, and eggs but only 1.5 kg (1500g) caster sugar and 1.5 kg (1500g) butter. We need to find the maximum number of cupcakes he can make given these sugar and butter constraints. 2. **Formula and rules:** The number of cupcakes is proportional to the amount of ingredients used. We calculate the maximum cupcakes based on each limiting ingredient separately and then take the minimum. 3. **Calculate maximum cupcakes from sugar:** $$\text{max cupcakes from sugar} = \frac{1500\text{g}}{30\text{g per 8 cupcakes}} \times 8$$ 4. Simplify the fraction: $$\frac{1500}{30} = 50$$ 5. Multiply by 8: $$50 \times 8 = 400$$ cupcakes from sugar. 6. **Calculate maximum cupcakes from butter:** $$\text{max cupcakes from butter} = \frac{1500\text{g}}{50\text{g per 8 cupcakes}} \times 8$$ 7. Simplify the fraction: $$\frac{1500}{50} = 30$$ 8. Multiply by 8: $$30 \times 8 = 240$$ cupcakes from butter. 9. **Determine the limiting ingredient:** The maximum cupcakes Jake can make is the minimum of the two values: $$\min(400, 240) = 240$$ cupcakes. 10. **Final answer:** Jake can make at most **240 cupcakes** with the available sugar and butter.