48.Kate's class has between 40 and 51 students. Exactly of 75%of the students in her class have black book bags, and exactly 1/6 of students in her class do not have a book bag at all. How many students are in Kate's class?
exactly 75%=3/4 implies the number is a multiple of 4, so the candidates are 40,44,48
exactly 1/6 implies it is also a multiple of 6, so
48 students
To find the number of students in Kate's class, we need to use the information given.
Let's assume the number of students in her class is x.
According to the given information, exactly 75% of the students in her class have black book bags. This can be expressed as 0.75x.
Also, exactly 1/6 of the students in her class do not have a book bag at all. This can be expressed as (1/6)x.
From the information given, we know that the number of students with black book bags and the number of students without any book bags should add up to the total number of students in her class (x).
Therefore, we can form the equation:
0.75x + (1/6)x = x
Simplifying the equation, we get:
(6/6)x + (1/6)x = x
(7/6)x = x
Now, we can solve for x by multiplying both sides of the equation by 6 to eliminate the fraction:
7x = 6x
x = 0
This means that there are 0 students in Kate's class, which doesn't seem possible. There might be a mistake in the question or additional information needed to solve it correctly.