In a science experiment, the temperature of a substance is measured at different times. The relationship between the temperature \( T \) (in degrees Celsius) and the time \( t \) (in minutes) is given by the linear equation \( T = 3t + 5 \). If the temperature of the substance is measured to be 35 degrees Celsius, how many minutes have passed since the start of the experiment? Let's think step by step and output the final answer within \boxed{}.
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