Completed question:
A school has two pathways through their math program. 2/3 of students follow the first path; the rest take the second
path. During one semester, 75% of the students who follow the first path pass it, while 90% of the students who follow the second path pass it. Follow the steps to find what fraction of students will pass math this semester.
a. Find the fraction of students who take the first path and pass:
b. Find the fraction of students who take the second path and pass:
c. Add the two fractions.
Answer:
a. 1/2
b. 3/10
c. 4/5
Step-by-step explanation:
The fraction of students that pass the semester is the sum of the fraction that passes the first path and the fraction that passes the second path.
a. If 2/3 of all students had taken the first step and only 75% passed, then, the fraction that passed is 75% of 2/3:
0.75 * (2/3)
1.5/3
1/2
b. The rest of the students got the second path. The total fraction of students is 1, so the fraction of students that took the second path was:
1 - (2/3)
(3 - 2)/3
1/3
And, 90% of these students had passed, so:
0.9 * (1/3)
0.9/3
0.3
3/10
c.
1/2 + 3/10 (The common minimus multiple between 2 and 10 is 20)
(10 + 6)/20
16/20 (dividing by 4)
4/5
