Answer:
18
Step-by-step explanation:
Given: There were [tex]45[/tex] runners to start a race. In the first half of the race, [tex]\frac{1}{3}[/tex] of them dropped out. In the second half of the race, [tex]\frac{2}{5}[/tex] of the remaining runners dropped out.
To Find: How many runners finished the race.
Solution:
Total number of runners [tex]=45[/tex]
Number of runners dropped out in first half of the race [tex]=\frac{1}{3}\text{of total}[/tex]
[tex]\frac{1}{3}\times45[/tex]
[tex]15[/tex]
Number of runners remaining after first half [tex]=\text{Total runners before first half}-\text{number of runners dropped out}[/tex]
[tex]45-15=30[/tex]
Number of runners dropped out in second half [tex]=\frac{2}{5}\text{of remaining after first half}[/tex]
[tex]\frac{2}{5}\times30[/tex]
[tex]12[/tex]
Number of runners who finished the race [tex]=\text{runners remaining after first half}-\text{runners dropped in second half}[/tex]
[tex]30-12=18[/tex]
Therefore [tex]18[/tex] runners finished the race.
