His weekly allowance is $20.
Explanation: Since he ended the week with $17 and we know he earned $7 from washing a car, he had $10 before he earned the extra $7. We know he spent half of his allowance at the movies, so $10 is half of the amount that he had before he went to the movies. $10 is half of $20, so his allowance is $20.
I hope I could help! :D