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?

One third of 84 is \(84 \times \frac{\mathrm{1} }{\mathrm{3}} = 84 \div 3 = 28\). 28 people 25 years old or younger applied for the job. Two seventh of 84 is \(84 \times \frac{\mathrm{2} }{\mathrm{7}} = 24\). 24 people who were at least 50 years old applied for the job. 84 - 28 - 24 = 32. 32 people applied for the job who were between 25 and 50.