Final answer:
To determine the ratio of Lilian's age to the total age, set Lilian's age as 2/3 of May's age and simplify the ratio, resulting in a final ratio of 2/5 or 40%.
Step-by-step explanation:
To find the ratio of Lilian's age to the total of Lilian's and May's ages combined, we can set up the ratio using algebra. Let's denote May's age as M and Lilian's age as L. According to the problem, L is 2/3 of M, or L = (2/3)M. The total age would then be L + M. To find the ratio of Lilian's age to their total age, we set up the following ratio: L / (L + M).
Plugging in the relationship between Lilian's and May's ages (L = (2/3)M), the ratio becomes (2/3)M / ((2/3)M + M). To simplify, factor out M in the denominator to obtain M[(2/3) + 1]. As a common denominator is 3, this simplifies to M(2/3 + 3/3) or M(5/3). The M's cancel out, leaving us with 2/5. So, Lilian's age is 2/5 or 40% of the total of both Lilian's and May's ages.