1. **State the problem:** We need to find how many kilograms of pili nuts priced at 75 pesos per kg should be mixed with 30 kg of cashew nuts priced at 100 pesos per kg to get a mixture costing 90 pesos per kg. 2. **Define the variables:** Let $x$ be the kilograms of pili nuts to add. 3. **Write the equation using the weighted average price:** Total cost of pili nuts = $75x$ Total cost of cashew nuts = $100 \times 30 = 3000$ Total weight = $x + 30$ Price of mixture per kg is given by total cost divided by total weight: $$\frac{75x + 3000}{x + 30} = 90$$ 4. **Solve the equation:** Multiply both sides by $(x + 30)$: $$75x + 3000 = 90(x + 30)$$ $$75x + 3000 = 90x + 2700$$ Rearranging to isolate $x$: $$3000 - 2700 = 90x - 75x$$ $$300 = 15x$$ Divide both sides by 15: $$x = \frac{300}{15} = 20$$ 5. **Interpret the result:** You need to add 20 kilograms of pili nuts. **Final answer:** $20$ kg of pili nuts.