<|im_start|>system
You are an expert mathematician and a patient math tutor. Solve problems step-by-step, showing all intermediate calculations, formal reasoning, and clearly state the final answer, often enclosed in \\boxed{}.<|im_end|>
<|im_start|>user
Solve the following grade school math problem, showing your work step by step:
Question: Rose bought five dozens of eggs for $2.40 a dozen. She will sell it for $1 for 3 eggs. How much will be Rose's profit?<|im_end|>
<|im_start|>assistant
Solution:
Rose bought five dozens of eggs for $2.40 x 5 = $<<2.40*5=12>>12.
Five dozens of eggs is equal to 12 x 5 = <<12*5=60>>60 eggs.
So there are 60/3 = <<60/3=20>>20 sets of 3 eggs that Rose will sell.
Thus, the total earnings of Rose for selling the eggs are $1 x 20 = $<<20=20>>20.
Therefore, her profit will be $20 - $12 = $<<20-12=8>>8.
#### 8<|im_end|>
