Question

a coach asked her athletes if they enjoy running. i only percent of the team do not like to run. of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. the diagram shows how the athletes are divided into subgroups. what is the total percentage of the athletes who do not enjoy cycling?

Explanation:

Step1: Assume the total number of athletes is 100.

Let the number of athletes who do not like running be \(x = 100\).

Step2: Calculate the number of athletes who do not like running and like cycling.

Since 70% of those who do not like running like cycling, the number of such athletes is \(0.7x=0.7\times100 = 70\).

Step3: Calculate the number of athletes who do not like running and do not like cycling.

The number of athletes who do not like running and do not like cycling is \((1 - 0.7)x=0.3x = 0.3\times100=30\).

Step4: Consider the proportion of those who like running.

Let's assume the proportion of those who like running is \(y\). We are not given information about \(y\) affecting the non - cycling part for non - runners, so we focus on the non - running group.
The percentage of athletes who do not enjoy cycling among all athletes (assuming we are only considering the non - running group for the sake of the information given) is 30% of the non - running group. But if we assume the whole group of athletes is considered and we have no other information about the running group's non - cycling preference, we just consider the non - running group's non - cycling part.

Answer:

30%