On a certain sightseeing tour the ratio of the number of children to the number of women was 2 to 5. What is the number of men on the tour?
1. On the tour, the ratio of number of children to number of men was 5 to 11

2. The number of women on the tour was less than 30

here's what you do:

* find the term or thing that's common to the 2 ratios ("children", in this case)

* MULTIPLY the ratios by appropriate factors (in exactly the same way you'd multiply the numerator and denominator of a fraction - because ratios, after all, are just glorified fractions) to generate that least common multiple in both

* combine the ratios

for statement (1) here, then:

the prompt tells us that C : W = 2 : 5, and statement (1) tells us that C : M = 5 : 11. the two C terms are 2 and 5, so the least common multiple is 10. multiply by 5's to give C : W = 10 : 25, and multiply by 2's to give C : M = 10 : 22. therefore, C : W : M = 10 : 25 : 22.

from this ratio, it's easy to see that the # of children must be a multiple of 10, the # of women must be a multiple of 25, and the # of men must be a multiple of 22.

combined with statement (2), this means that the numbers must actually be 10, 25, and 22, since any multiple thereof would be way too big to satisfy the "under 30" criterion.