1. State the problem: We need to find how many peanuts are required to make 5.1 kg of peanut butter, given that 540 peanuts make 340 g of peanut butter. 2. Convert 5.1 kg to grams because the given data uses grams: 5.1 kg = 5.1 \times 1000 = 5100 \text{ g}. 3. Set up a proportion to find the number of peanuts for 5100 g. If 540 peanuts make 340 g, then $ x $ peanuts make 5100 g: $$ \frac{540}{340} = \frac{x}{5100} $$ 4. Solve for $ x $: $$ x = \frac{540 \times 5100}{340} $$ 5. Calculate the value: $$ x = \frac{540 \times 5100}{340} = \frac{2,754,000}{340} = 8100 $$ 6. Final answer: It would take 8100 peanuts to make 5.1 kg of peanut butter.