At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour during regular time. During overtime Thomas gets paid 1.5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas's pay for this week remains?

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Thomas makes $15 per hour for 40 hours.

$$ 15(40) $$

Thomas makes $15(1.5) per hour for 6 hours during overtime.

$$ 15(1.5)(6) $$

After taking $117 out:

$$ 15(40) + 15(1.5)(6) - 117 $$ $$ 600 + 135 -117 $$ $$ 600 + 18 $$ $$ = \boxed{618} $$