Derek caught the ball 2 * 23 - 4 = 46 - 4 = <<2*23-4=42>>42 times.

Tammy caught the ball 42 / 3 + 16 = 14 + 16 = <<42/3+16=30>>30 times.

# Answer

30
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Joe played catch with Derek and Tammy. He caught the ball 23 times. Derek made four less than double the catches Joe did. Tammy caught the ball sixteen more than a third of the times Derek did. How many times did Tammy catch the ball?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
30
Joe played catch with Derek and Tammy. He caught the ball 23 times. Derek made four less than double the catches Joe did. Tammy caught the ball sixteen more than a third of the times Derek did. How many times did Tammy catch the ball?
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