"He was penalized with 10 dollars fine" is it correct?
Can somebody tell if it's correct, and provide some alternatives sentences to deliver the same meanings?

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I would change it to "a 10 dollar fine". 
Other alternates:
He was punished with a 10 dollar fine.
He was given a 10 dollar fine. 
There was an added 10 dollar penalty.

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He was given a ten dollar fine.

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penalized with a fine of?

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I would suggest any of these:

"He was fined $10."

"His penalty was a $10 fine."

"As a penalty, he was fined $10."

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Thanks, Tuyet and Nadia for the contribution.