Out of the 400 emails, 1/4*400 = <<400*1/4=100>>100 emails were spam emails.

The number of emails that were not spam emails is 400-100 = <<400-100=300>>300

2/5 of the emails which were not spam were promotional emails, a total of 2/5*300=<<2/5*300=120>>120 emails.

If the rest of the emails were important emails, there were 300-120 = <<300-120=180>>180 important emails.

# Answer

180
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Out of the 400 emails that Antonia received in her mail, 1/4 were spam emails, while 2/5 of the remaining emails were promotional messages. If the rest of the emails were important emails, calculate the total number of important emails in her inbox.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
180
Out of the 400 emails that Antonia received in her mail, 1/4 were spam emails, while 2/5 of the remaining emails were promotional messages. If the rest of the emails were important emails, calculate the total number of important emails in her inbox.
train