<|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: Three people divided an amount of $1920. The second took $80 more than the first and the third took twice what the second took. Calculate the share of the first one.<|im_end|>
<|im_start|>assistant
Solution:
Let X be the amount of what the first took.
The second took X+<<+80=80>>80.
The third took (X+80)*2.
The total amount X + (X+80) + (X+80)*2 = 1920.
X + X + 80 + 2*X + 80*2 = 1920
X*4 + 240 = 1920.
X*4 = 1680.
X = <<420=420>>420.
#### 420<|im_end|>
