Question

One third of the candidates for a job were 25 years old or younger. two sevenths of the candidates were at least 50 years old. if 84 people applied for the job, how many were between 25 and 50?

Answer 1

There are three groups of people: 25 years old and younger, between 25 to 50, and 50 years old and older. Their fractions must equal to 1 because these three together form the whole.

1 = 1/3 + 2/7 + x
where x is the fraction for people ages 25 to 50 years old
x = 8/21

So, the actual number of people ages 25 to 50 years old is:

84(8/21) = 32 people