In a science class, 40% of the students received a grade of A, 30% received a grade of B, and 20% received a grade of C on a project. The others fell short of a passing grade. a. If 12 students received an A, how many students were in the science class? b. How many students received a failing grade?

a. So we know that 40% of the class have received an A and that is equal to 12 students. Lets call the entire class an X number of students since we don't know how many students are there. Lets try to create a simple ratio to find out how many students were there. The entire class will obviously be 100% of the X.

If 40% is 12 students.

Then 100% is X students.

Lets cross multiply, so we will have 40 times x equal to 100 times 12.

40x=12*100

40x=1200

Divide both sides with 40.

40x/40 = 1200/40

x=30 students.

b. We know that 40% received A, 30% got B and 20% got C. The rest didn't pass. So lets try and add the percentage together and subtract that from the 100% of the entire class.

40+30+20=90% of the class

100-90=10% of the class did not pass.

If 100% is 30 students

Then 10% is Y students.

Cross-multiplying will give us 100 times Y equal to 10 times 30.

100y=300

Divide both sides with 100.

100y/100 = 300/100

y=3 students.