In a class of boys and girls, 5/6 of students passed the test and 6 failed the test. If 4/9 of the students who passed the test are girls how many boys passed the test
To find out how many boys passed the test, we need to calculate the number of students who passed the test, the number of girls who passed the test, and then subtract the number of girls from the total number of students who passed.
Let's assign variables to the unknowns:
Let's say the total number of students in the class is represented by 'x'.
Let 'a' represent the number of students who passed the test.
Let 'b' represent the number of girls who passed the test.
Let 'c' represent the number of boys who passed the test.
According to the given information:
5/6 of students passed the test, and 6 students failed the test.
So, the number of students who passed the test (a) is equal to 5/6 of the total number of students (x).
a = (5/6) * x
4/9 of the students who passed the test are girls.
So, the number of girls who passed the test (b) is equal to 4/9 of the total students who passed the test (a).
b = (4/9) * a
The number of boys who passed the test (c) is equal to the total number of students who passed the test (a) minus the number of girls who passed the test (b).
c = a - b
Now, let's substitute the value of a from equation 1 into equation 2:
b = (4/9) * [(5/6) * x]
= (4/9) * (5/6) * x
Finally, let's substitute the value of b from equation 2 into equation 3:
c = [(5/6) * x] - [(4/9) * (5/6) * x]
To find the value of c (boys who passed the test), we can plug in the value of x (total number of students) into the equation.
Please provide the value of x (total number of students) to calculate the number of boys who passed the test.