A school has two pathways through the math program. At this school, 3/4 of students follow the first path, and the rest take the second path. During one semester, 80% of the students who follow the first path pass the program, while 20 % of the students who follow the second path pass it. Find the fraction of students who take the first path and pass.

3/5 of students who take the first path and pass

Step-by-step explanation:

* Lets explain how to solve the problem

- There are two pathways through the math program

- At this school 3/4 of students follow the first path

- The rest take the second path

- During one semester, 80% of the students who follow the first path

pass the program

- 20 % of the students who follow the second path pass it

- We want to know the fraction of students who take the first path

and pass

* Lets solve the problem

∵ 3/4 of students follow the first path

∵ The rest take the second path

∴ The fraction of the rest = 1 - 3/4 = 1/4

∴ 1/4 of the students follow the second path

∵ 80% of the students who follow the first path pass the program

∵ 80% = 80/100 = 8/10 = 4/5

∵ 4/5 of the students who follow the first path pass the program

∵ 3/4 of students follow the first path

∴ 4/5 of 3/4 of the students of the first path pass

∵ 4/5 of 3/4 = 3/5

∴ 3/5 of students who take the first path and pass