A total of 11 400 people entered a running race - HSC - SSCE Mathematics Standard - Question 15 - 2021 - Paper 1

Given the ratio of professional to amateur runners is 3:16, we can sum the parts: 3 + 16 = 19 parts.

The number of professional runners can be calculated as:

ext{Number of Professional Runners} = rac{3}{19} imes 11,400 = 1,800

Now, we can find the total number of amateurs:

ext{Number of Amateurs} = rac{16}{19} imes 11,400 = 9,600

Since 600 amateurs did not complete the race, the number of amateurs who completed the race is:

$9,600 - 600 = 9,000$

The desired ratio of professional runners to amateurs who completed the race is:

ext{Ratio} = rac{1,800}{9,000} = rac{1}{5}