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

To find the number of candidates between 25 and 50 years old, we need to subtract the candidates who are 25 years old or younger and those who are at least 50 years old from the total number of candidates. The calculation yields zero candidates between 25 and 50 years old.

Step-by-step explanation:

To find the number of candidates between 25 and 50 years old, we need to subtract the candidates who are 25 years old or younger and those who are at least 50 years old from the total number of candidates.

Let's start by finding the number of candidates who are 25 years old or younger. We are given that one third of the candidates fall into this age group. So, we can set up the equation:

1/3 * Total number of candidates = Number of candidates who are 25 years old or younger

Let's solve for the number of candidates who are 25 years old or younger:

1/3 * Total number of candidates = 84

Total number of candidates = 84 * 3 = 252

Now, let's find the number of candidates who are at least 50 years old. We are given that two sevenths of the candidates fall into this age group. So, we can set up the equation:

2/7 * Total number of candidates = Number of candidates who are at least 50 years old

Let's solve for the number of candidates who are at least 50 years old:

2/7 * Total number of candidates = ?

To find the missing value, we can subtract the number of candidates who are 25 years old or younger from the total number of candidates:

Total number of candidates - Number of candidates who are 25 years old or younger = Number of candidates who are at least 50 years old

252 - 84 = Number of candidates who are at least 50 years old

Number of candidates who are at least 50 years old = 168

Finally, to find the number of candidates between 25 and 50 years old, we can subtract the number of candidates who are 25 years old or younger and those who are at least 50 years old from the total number of candidates:

Total number of candidates - Number of candidates who are 25 years old or younger - Number of candidates who are at least 50 years old = Number of candidates between 25 and 50 years old

252 - 84 - 168 = Number of candidates between 25 and 50 years old

Number of candidates between 25 and 50 years old = 252 - 252 = 0

Therefore, there were no candidates between 25 and 50 years old.

Answer 2

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