To find out how many days it will take Nigel to sell 36 candy bars at a rate of 4 bars every 3 days, we first determine how many bars he sells per day.
Nigel sells: \[ \frac{4 \text{ bars}}{3 \text{ days}} = \frac{4}{3} \text{ bars per day} \]
Next, we need to calculate how many days it will take him to sell 36 candy bars. We can set up the following equation: \[ \text{Number of days} = \frac{\text{Total bars}}{\text{Bars per day}} = \frac{36 \text{ bars}}{\frac{4}{3} \text{ bars per day}} \]
To divide by a fraction, we multiply by its reciprocal: \[ \text{Number of days} = 36 \times \frac{3}{4} = \frac{36 \times 3}{4} = \frac{108}{4} = 27 \]
Thus, it will take Nigel 27 days to sell all 36 candy bars.