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?

If the cost per kilogram of the cashews were $2.50, then the total cost for 1.5 kilograms would only be $3.75. This would not be equal to the total cost of the Brazil nuts since the costs must be equal, and it would not support a selling price that is 50% higher than the total cost of the mixture.

At a rate of $7.67 per kilogram for the cashews, the total cost would be approximately $11.50 for 1.5 kilograms. This value is still not equal to the total cost of the Brazil nuts, leading to an imbalance in the costs and making it impossible to meet the condition of selling at 50% above the total cost.

If the cost of the cashews were $15 per kilogram, the total cost for 1.5 kilograms would be $22.50. This would significantly exceed the potential total cost of the Brazil nuts, creating a discrepancy in the equal cost requirement and making it impossible to achieve the correct selling price.

With a cost of $30 per kilogram, the total cost for the cashews would be $45 for 1.5 kilograms. This would create an even larger imbalance in the costs compared to the Brazil nuts, making it impossible for the total selling price to reflect a 50% increase over the total cost of the mixture.