To find out how many times Delon can ride the roller coaster, we first need to calculate how many tickets he has left after using the 4 tickets for the carousel.
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Start with the total number of tickets: \[ 37 \text{ tickets} \]
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Subtract the tickets used for the carousel: \[ 37 - 4 = 33 \text{ tickets left} \]
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Since each ride on the roller coaster uses 3 tickets, we divide the remaining tickets by the number of tickets per ride: \[ \frac{33}{3} = 11 \]
Delon can ride the roller coaster 11 times.
Therefore, the answer is 11.