There were 84 runners to start a race. In the first half of the race, \( \frac{1}{4} \) of them dropped out. In the second half of the race, \( \frac{1}{3} \) of the remaining runners dropped out. How many runners finished the race?

Let's break it down step-by-step! Initially, there were 84 runners. In the first half of the race, \(\frac{1}{4}\) of them dropped out: \[ \text{Runners who dropped out in the first half} = \frac{1}{4} \times 84 = 21 \] So, the number of runners remaining after the first half is: \[ \text{Runners remaining} = 84 - 21 = 63 \] In the second half of the race, \(\frac{1}{3}\) of the remaining runners dropped out: \[ \text{Runners who dropped out in the second half} = \frac{1}{3} \times 63 = 21 \] Thus, the number of runners finished the race is: \[ \text{Runners finished} = 63 - 21 = 42 \] Therefore, 42 runners finished the race.