Let's denote Mrs. Lee's earnings in May as \( M \) and the rest of the family's income as \( F \). The total family income in May would then be \( M + F \).

In June, Mrs. Lee earned 20 percent more than in May, so her earnings in June would be \( M + 0.20M = 1.20M \). The rest of the family's income remained the same, so the total family income in June would be \( 1.20M + F \).

According to the information given, Mrs. Lee's earnings in June were approximately 54.54545454545454 percent of the Lee family's total income. Therefore, we can write the following equation:

\[ 1.20M = 0.5454545454545454 \times (1.20M + F) \]

To find the percentage of Mrs. Lee's earnings in May, we need to solve for \( M \) in terms of \( M + F \) and then convert that to a percentage. Let's solve the equation:

\[ 1.20M = 0.5454545454545454 \times (1.20M + F) \]
\[ 1.20M = 0.5454545454545454 \times 1.20M + 0.5454545454545454 \times F \]
\[ 1.20M - 0.5454545454545454 \times 1.20M = 0.5454545454545454 \times F \]
\[ M \times (1.20 - 0.5454545454545454 \times 1.20) = 0.5454545454545454 \times F \]
\[ M \times (1.20 - 0.6545454545454545) = 0.5454545454545454 \times F \]
\[ M \times 0.5454545454545455 = 0.5454545454545454 \times F \]
\[ M = F \]

This means that Mrs. Lee's earnings in May were equal to the rest of the family's income. Therefore, Mrs. Lee's earnings were 50 percent of the Lee family's total income in May, because her earnings (M) were equal to the rest of the family's income (F), making the total income \( M + F = 2M \), and \( M \) is half of \( 2M \).
5월의 이 씨의 수입을 \( M \), 나머지 가족의 수입을 \( F \), 5월의 총 가족 수입을 \( M + F \), 6월의 이 씨의 수입을 \( M + 0.20M = 1.20M \), 나머지 가족의 수입은 동일하게 유지되므로 6월의 총 가족 수입은 \( 1.20M + F \), 6월의 이 씨의 수입은 총 수입의 약 54.5454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454