One third of the students in mrs. hayko's class walk to school. Of the students who do not walk, four-fifths take the bus.

a) what fraction of the students in Mrs. Hayko's class take the bus to school?

b) How many students might there be in her class?

So 2/3 of her students do NOT walk to school

of those (4/5) take the bus

so (4/5)(2/3) or 8/15 take the bus

The number of students must be a multiple of 15

In an enlightened board of education she would have 15 students,
in reality she probably has 30 students,
and , in some backwards regions, she could have 45 students.

Step 1: Let's assume there are a total of x students in Mrs. Hayko's class.

Step 2: One third of the students walk to school, which means (1/3) * x students walk.

Step 3: The remaining students do not walk. Out of these students, four-fifths take the bus, which means (4/5) * (2/3) * x students take the bus.

a) To find the fraction of students who take the bus, we add the fractions: (1/3) * x + (4/5) * (2/3) * x
Simplifying the expression: (1/3) * x + (8/15) * x
Finding a common denominator and adding the fractions: (5/15) * x + (8/15) * x = (13/15) * x

Therefore, the fraction of students who take the bus is 13/15.

b) To find the possible number of students in Mrs. Hayko's class, we can use any multiple of x, since the value of x was arbitrary.

Therefore, the number of students in her class might be 15x, where x is any positive integer.

a) To find the fraction of students who take the bus to school, we need to find the fraction of students who do not walk and then determine how many of them take the bus.

First, let's calculate the fraction of students who do not walk to school. Since one-third of the students walk, two-thirds do not walk. So the fraction of students who do not walk to school is 2/3.

Next, we need to find the fraction of students who take the bus among those who do not walk. Given that four-fifths of the non-walking students take the bus, we can express this fraction as 4/5.

Now, we multiply the fraction of non-walking students by the fraction of non-walking students who take the bus: (2/3) * (4/5). This simplifies to (8/15).

Therefore, the fraction of students in Mrs. Hayko's class who take the bus to school is 8/15.

b) To determine the number of students in Mrs. Hayko's class, we need additional information. The current problem does not provide any information connecting the fraction of students who walk or take the bus to the total number of students in the class. Without this information, we cannot determine the exact number of students in her class.

the answer will be 1/32