QUESTION
There are two groups of students in the sixth grade. There are 30 students in group A, and 50 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 12% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
ANSWER SELECTION
(A) 13%
(B) 14$
(C) 15% (CORRECT)
(D) 16%
(E) 17%
EXPLANATION
To find the percentage of all sixth graders who forgot their homework, we need to divide the number who forgot their homework by the total number of students in the class. There are 30 students in group A and 50 students in group B, so there are 30 + 50 = 80 total students in both groups.
Since 20% of the 30 students in group A forgot their homework and 20% is equivalent to 0.20, we know that (0.20)(30) = 6 students in group A forgot their homework. Similarly, 12% of the 50 students in group B forgot their homework, so (0.12)(50) = 6 students in this group forgot their homework. In total, 6 + 6 = 12 students forgot their homework.
So, the fraction of all students who forgot their homework is 12/80 . Dividing the numerator and denominator by 4, this fraction becomes 3/20, which is equivalent to 0.15, or 15%. So, choice (C) is correct.
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