16. A grocer mixed 1.5 kilograms of cashew nuts with 6 kilograms of Brazil nuts and sold the mixture at $1.50 per 0.25-kilogram bag. To the grocer the total cost of the cashews was equal to the total cost of the Brazil nuts. If the entire mixture was sold for 50 percent more than the total cost of the nuts to the grocer, what was the cost per kilogram of the cashews to the grocer?
Answer: C
The cost per kilogram of the cashews to the grocer is $10.
The cost per kilogram of the cashews to the grocer is determined to be $10. This conclusion is reached by analyzing the total costs and selling price of the nut mixture.
A) 2.5
This option is incorrect because if the cost of cashews were $2.50 per kilogram, the total cost of the cashews (1.5 kg) would be $3.75. Given that the total costs of cashews and Brazil nuts are equal, the Brazil nuts would also need to have a total cost of $3.75, which is inconsistent with the overall pricing of the mixture.
B) 7.67
This option is incorrect. If cashews cost $7.67 per kilogram, the total cost of the cashews would be approximately $11.50. This would require the Brazil nuts to also cost $11.50, leading to a total cost of $23.00. Selling the mixture at a price 50% higher than this total would not align with the selling price per bag calculated from the mixture.
C) 10
This option is correct. If the cost of cashews is $10 per kilogram, the total cost of the cashews would be $15 (1.5 kg × $10/kg). Since the total cost of the Brazil nuts must equal this, it also implies that the Brazil nuts cost the grocer $15. The total cost of the mixture is thus $30. Selling it at 50% more results in a selling price of $45, which matches the price calculated from selling 180 bags at $1.50 each.
D) 15
This option is incorrect. If the cost of cashews were $15 per kilogram, the total cost would be $22.50. This would mean the Brazil nuts also cost $22.50, leading to a total cost of $45. Selling the mixture at 50% more would require a selling price of $67.50, which does not match the calculated selling price based on the bag price.
E) 30
This option is incorrect. If the cost of cashews were $30 per kilogram, the total cost of the cashews would be $45. This would necessitate the Brazil nuts to also cost $45, resulting in a total cost of $90. Selling it at 50% more would lead to a price of $135, which is not consistent with the selling price derived from the mixture.
Conclusion
The cost per kilogram of the cashews is definitively $10, as it aligns with the equal cost condition of the nuts and the overall pricing strategy of the grocer. All other options fail to meet the necessary conditions for total costs and selling prices, confirming that $10 is the only viable solution.