Since Kenneth spent 10%, then he is left with 100% - 10% = 90% of his earnings.

Since 90% of his earnings is worth $405, then 1% of his earnings is $405/90 = $<<405/90=4.50>>4.50.

Hence, Kenneth's earnings is $4.50 x 100 = $<<450=450>>450.

# Answer

450
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Kenneth spent 10% of this earnings this week on a new joystick. If he is left with $405, how much were his earnings?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
450
Kenneth spent 10% of this earnings this week on a new joystick. If he is left with $405, how much were his earnings?
train