Math problem of the day

Question:
There are two grade 8 classes in a school. 70% of the students in the first class passed a test, and 80% of the students in the second class passed the same test. If there are 50 students in all, and the first class has 10 students more than the second class, what percentage of all students passed the test?

Answers variants: A. 70   B. 71   C. 72   D. 73   E. 74


Correct answer: E. 74
Tutorial:

Let x be the number of students in the first class and y the number of students in the second class.
We find x and y.
x + y = 50 and
x - y = 10
Adding these equations, we find that
2x +y -y = 50+10,
2x = 60 and so
x = 30
Then y = 30 - 10 = 20
So, taking into account both classes,
0.7*30 + 0.8*20 = 21 + 16 = 37 students passed.
Therefore 37/50 = 0.74 or 74%,
so the correct answer is (E) 74%.

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