At a school, of the students participate in music programs. Of the students who do not participate in music programs, participate in athletics. What percent of all students participate in neither music programs nor athletics?
For a percentage that applies to a subgroup, first identify the size of that subgroup before calculating the percentage. Using a total of makes the interpretation especially efficient: convert each percentage of all students into a count, apply the conditional percentage to the appropriate remaining group, and then express the final count as a percent of .
Hints
Choose a convenient total
Imagine that the school has students. Then a percentage of all students can be treated as a number of students.
Identify the remaining group
First determine how many students do not participate in music programs. The athletics percentage applies only to this remaining group.
Use the conditional percentage
Find of the students who are not in music programs. Then subtract that group from the students who are not in music programs.
Desmos Guide
Calculate using a total of 100 students
In a Desmos expression line, enter 100 - 40 - 0.25(100 - 40). The result is the number of students, out of , who participate in neither activity. Because the total is , the result is also the required percent.
Step-by-step Explanation
Use a total of 100 students
Assume the school has students. Then each number of students corresponds directly to the same percent of all students.
Find the students not in music programs
Since of the students participate in music programs, students participate in music programs.
Therefore, students do not participate in music programs.
Find the athletics participants among the remaining students
Of the students who do not participate in music programs, participate in athletics:
So students participate in athletics but not in music programs.
Find the students in neither activity
The students who participate in neither activity are the students who are not in music programs and also are not in athletics:
Out of students, this is . Therefore, the correct answer is (Choice C).