珍妮丝在1月份卖了80个蛋糕。2月份，她比1月份多卖了30个这样的蛋糕。

1. Calculate the percentage increase

$\text{Percentage increase} = \frac{\text{Increase}}{\text{Original}} \times 100\%$
$\text{Percentage increase} = \frac{30}{80} \times 100\% = 37.5\%$

1. Find the number of cakes sold in February

$80 + 30 = 110$

2. Calculate the number of cakes sold in March after a 100% increase

$110 + (100\% \times 110) = 110 + 110 = 220$
Alternatively, $110 \times 2 = 220$

1. Calculate the number of cakes sold in April

Number of cakes sold in January = $80$
Decrease = $40\%$
Number of cakes sold in April = $80 \times (1 - 0.40) = 80 \times 0.60 = 48$

2. Determine the maximum possible total for April and May

The total number of cakes sold in April and May, when rounded to the nearest hundred, is $200$.
The greatest possible total before rounding is $249$.

3. Calculate the greatest possible number of cakes sold in May

Greatest possible number of cakes sold in May = $249 - 48 = 201$